157 results on '"Y P Varshni"'
Search Results
2. Critical temperatures of elements from their boiling points
- Author
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Y. P. Varshni
- Subjects
chemistry.chemical_element ,Thermodynamics ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Boiling point ,chemistry ,Group (periodic table) ,Acentric factor ,Materials Chemistry ,Linear relation ,Physical and Theoretical Chemistry ,Tellurium ,Nucleate boiling ,Polonium - Abstract
A linear relation between critical temperature and boiling point is proposed for elements belonging to the same group in the periodic table. The validity of the relationship is demonstrated for the alkalies and the groups 16, 17 and 18. From this the critical temperature of tellurium is predicted as 2325 K and that for polonium as 2277 K.
- Published
- 2007
3. Two electrons in a simple harmonic potential
- Author
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S H Patil and Y P Varshni
- Subjects
Physics ,Hookes Law Model ,Systems ,General Physics and Astronomy ,Electron ,Eigenfunction ,Simple harmonic motion ,Magnetic field ,Simple (abstract algebra) ,2-Electron Atom ,Quantum mechanics ,Magnetic-Field ,Wave function ,Energy (signal processing) ,Eigenvalues and eigenvectors - Abstract
Some structural properties of energy eigenfunctions of two electrons in a simple harmonic potential are analyzed. Simple expressions are obtained for the energy spectrum based on a model potential, and on a model wave function. These expressions give accurate values for the energy eigenvalues and provide a physical insight into their structure.PACS Nos.: 3.65.Ge, 73.21.La, 78.67.Hc
- Published
- 2006
4. Hydrogenic system in an off-centre confining oscillator potential
- Author
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Y. P. Varshni and S H Patil
- Subjects
Physics ,Impurity States ,Boundary-Conditions ,General Physics and Astronomy ,Electron ,Atom ,Satisfy ,Displacement (vector) ,Perturbation-Theory ,Cell Model ,Gaas-Ga1-Xalxas ,Perturbation theory (quantum mechanics) ,Boundary value problem ,Atomic physics ,Ground state ,Wave function ,Wave-Functions ,Spherical Quantum-Dot ,Elliptic coordinate system - Abstract
The hydrogenic system, confined in an off-centre oscillator potential, is separable in terms of elliptic coordinates. Its general properties are analysed and energies are obtained for some states, for some values of displacement and potential strength. A model wave function is developed and used to obtain the energies and polarizabilities for the ground state. PACS Nos.: 03.65.Ge, 73.21.La, 78.67.Hc
- Published
- 2004
5. A simple description of the spectra of confined hydrogen, helium, and lithium
- Author
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Y P Varshni and S H Patil
- Subjects
Physics ,Enclosed Quantum-Systems ,Hydrogen ,Dot ,General Physics and Astronomy ,chemistry.chemical_element ,Hydrogen atom ,Electron ,High-Pressures ,Effective nuclear charge ,Spectral line ,Perturbation-Theory ,chemistry ,Cell Model ,2-Electron Atoms ,Gaas-Ga1-Xalxas ,Lithium ,Physics::Atomic Physics ,Direct Variational Method ,Atomic physics ,Perturbation theory ,Wave-Functions ,Helium - Abstract
A simple description of the spectrum of confined hydrogen atom is obtained in terms of an scheme involving interpolation between the expressions for large and small values of the confining radius. Satisfactory agreement is shown to exist between the eigen energies thus calculated and exact values. The scheme is extended for helium and lithium. With the simulation of interaction between the electrons by a screened nuclear charge, some energy levels are deduced for the confined helium and lithium.PACS Nos.: 03.65.Ge, 73.21.La, 78.67.Hc
- Published
- 2004
6. Wave functions for the hydrogen atom in a dense plasma
- Author
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Y. P. Varshni
- Subjects
Physics ,Dipole ,Oscillator strength ,Polarizability ,General Physics and Astronomy ,Physics::Atomic Physics ,Radius ,Hydrogen atom ,Plasma ,Atomic physics ,Absorption (electromagnetic radiation) ,Wave function - Abstract
A hydrogen atom in a high-density plasma is simulated by a model in which the hydrogen atom is confined in an impenetrable spherical box, with the atom at the centre. For the protonelectron interaction the DebyeHuckel potential is used. Variational wave functions are proposed for the 1s and 2p states. Energies calculated from these for different values of the radius of box (r0) are shown to be in good agreement with the exact values. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s [Formula: see text] 2p transition and the dipole polarizability for different values of r0. PACS Nos.: 03.65.Ge, 32.70.Os, 31.70.Dk, 52.20.j
- Published
- 2003
7. Wentzel–Kramers–Brillouin quantization rules for two-dimensional quantum dots
- Author
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Rajkumar Roychoudhury, Anjana Sinha, and Y. P. Varshni
- Subjects
Physics ,Mesoscopic physics ,Semiclassical physics ,Eigenfunction ,Condensed Matter Physics ,WKB approximation ,Electronic, Optical and Magnetic Materials ,Quantization (physics) ,Classical mechanics ,Central force ,Quantum mechanics ,Electrical and Electronic Engineering ,Wave function ,Harmonic oscillator - Abstract
In this paper, we apply the semiclassical Wentzel–Kramers–Brillouin (WKB) approximation to an electron in a central force potential, confined in a two-dimensional disc, and we obtain the quantization rules for such a system. As explicit examples, we consider the two most widely studied potentials, viz., the parabolic potential (the harmonic oscillator) and the Hydrogenic impurity state (Coulomb potential) in two dimensions. Both the systems are confined within an impenetrable circular wall of radius r0: In particular, we determine the energies as well as eigenfunctions by this approach. On comparing these energies with those from exact numerical values, the agreement is found to be quite good. Moreover, the WKB approach is found to give a good estimate of the wave functions as well. These results suggest that the WKB approximation works well even for such rigid wall spatial confinement and the present approach can be applied to other confined systems such as those which are encountered in mesoscopic physics. r 2002 Elsevier Science B.V. All rights reserved.
- Published
- 2003
8. Scaling Relation For The Energy Levels Of A Hydrogen Atom At High Pressures
- Author
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Y. P. Varshni
- Subjects
Condensed Matter::Quantum Gases ,SIMPLE (dark matter experiment) ,Chemistry ,High pressure ,General Physics and Astronomy ,Physics::Atomic Physics ,Hydrogen atom ,Radius ,Physical and Theoretical Chemistry ,Atomic physics ,Scaling ,Mathematical Physics ,Energy (signal processing) - Abstract
The effect of high pressure on a hydrogen atom has frequently been simulated by enclosing the atom in an impenetrable spherical box. It is shown that for such a confined hydrogen atom placed at the centre of a spherical box a simple scaling relation exists between the energy and the radius of the confining box for 1s, 2p, 3d, and 4f levels, and another similar relation exists for 2s, 3p, and 4d levels.
- Published
- 2002
9. Excited states of two-dimensional excitons in quantum wells
- Author
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Y. P. Varshni
- Subjects
Physics ,Theoretical physics ,Exciton ,Excited state ,General Physics and Astronomy ,Atomic physics ,Free carrier ,Quantum well ,WKB approximation - Abstract
The energies of ten excited states of screened two-dimensional excitons in a semiconducting quantum-well structure are calculated as a function of the screening parameter qs by the WKB method. The screening of the Coulomb interaction between the electron-hole pair by the free carriers present is taken into account by using the screened potential obtained by Stern and Howard (1967). The energies of the excited states are found to decrease with increasing values of the screening parameter qs in all cases. Further the levels become unbound at finite values of the screening parameter. Critical screening parameters are estimated for the ten states. PACS Nos.: 73.21Fg, 78.67De, 71.35-y, 71.35Cc Resume : Nous presentons un calcul WKB pour les energies de dix etats excites d'excitons blindes (ecran) en 2-D dans un puits quantique de semi-conducteur, en fonction du parametre d'ecran qs. L'interaction de Coulomb avec ecran entre les paires electron-trou par les porteurs de charges libres est decrit par le potentiel avec ecran de Stern et Howard (1967). Dans tous les cas, nous trouvons que les energies d'excitation decroissent lorsqu'augmente le parametre qs. De plus, les etats excites cessent d'etre lies pour des valeurs finies de qs. Nous donnons les valeurs critiques du parametre qs pour les dix etats. (Traduit par la Redaction)
- Published
- 2002
10. Walker, Arthur Geoffrey
- Author
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Kenneth W. Ford, Mark Hurn, Thomas D. Kinman, John McFarland, Trudy E. Bell, Malcolm R. Forster, Ian T. Durham, John Rogers, Wayne Orchiston, Fernand Hallyn, Michael S. Reidy, Petr Hadrava, Michael Rich, David Jefferies, Fathi Habashi, Virginia Trimble, Craig B. Waff, Donald K. Yeomans, Richard P. Wilds, Jordan D. Marché, Solange Grillot, László Szabados, Martin Solc, Robert Alan Hatch, Alena Hadravová, Benno van Dalen, Paul Charbonneau, John Hearnshaw, Mihkel Joeveer, Christian E. Hauer, Christof A. Plicht, Thomas R. Williams, Stephen D. Snobelen, Sallie Baliunas, Peter Broughton, Robinson M. Yost, M. Colleen Gino, Eugene F. Milone, Oliver Knill, Lodewijk Woltjer, Dennis Danielson, Thomas Dobbins, William Sheehan, Jeff Suzuki, Douglas Scott, Daniel Kolak, Scott W. Teare, Guo Shirong, Y. P. Varshni, Gary A. Wegner, Jürgen Hamel, Anneliese Schnell, David W. Dewhirst, Roy H. Garstang, Charles H. Smith, Frieda A. Stahl, Daniel W. E. Green, Richard Baum, Thomas A. Dobbins, Adam Mosley, Cindy Lammens, and Alan H. Batten
- Subjects
Physics - Published
- 2014
11. Būzjānī: Abū al-Wafā’ Muḥammad ibn Muḥammad ibn Yaḥyā al-Būzjānī
- Author
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Jeff Suzuki, Jordan D. Marché, Robert Alan Hatch, Jan Mietelski, Alex Dalgarno, Glenn A. Walsh, Kevin J. Kilburn, Y. Tzvi Langermann, Thomas R. Williams, Jacques Lévy, Edward Baron, Dorrit Hoffleit, Thomas J. Bogdan, Matthew F. Dowd, Peter Wlasuk, Jean‐Louis Trudel, Steven Turner, Behnaz Hashemipour, Kristian Peder Moesgaard, Alan H. Batten, Patrick A. Catt, Paul Couteau, Wolfgang Kokott, Gyula Klima, Mary Croarken, James M. Lattis, Julian Holland, Benno van Dalen, Gustav Holmberg, Guenther Görz, Michio Yano, Monique Gros, Martin Solc, Keith Snedegar, Patricia S. Whitesell, Raymonde Barthalot, Ednilson Oliveira, Christian Nitschelm, Jürgen Hamel, Roy H. Garstang, Marvin Bolt, Ian T. Durham, Virginia Trimble, Hartmut Frommert, Alexander A. Gurshtein, Alan W. Hirshfeld, Dennis Danielson, Thomas A. Dobbins, Robert J. Hurry, Daniel Kolak, Y. P. Varshni, Antonio Ten, Robert K. DeKosky, Suzanne Débarbat, John Hearnshaw, Alastair G. Gunn, Françoise Launay, Marilyn Bailey Ogilvie, Davide Neri, Robert D. McGown, Solange Grillot, Helmut A. Abt, Richard A. Jarrell, Richard Baum, Gerald P. Verbrugghe, Jean‐Pierre Luminet, Audouin Dollfus, Voula Saridakis, Alv Egeland, Steven N. Shore, Ronald Florence, Graham Hall, Michael Fosmire, Josep Casulleras, Raghini S. Suresh, Takanori Kusuba, William Sheehan, Peter Broughton, Alistair Kwan, Robert McGown, Stephen Gaukroger, Craig B. Waff, Grant Christie, Yuri V. Balashov, Eugene F. Milone, Julio Samsó, Gary L. Cameron, Raymond E. White, Roger Cayrel, Joseph F. MacDonnell, Ian Elliott, Oliver Knill, and Hidemi Takahashi
- Subjects
Philosophy - Published
- 2014
12. Biela, Wilhelm Freiherr von
- Author
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Jürgen Hamel, Ronald Florence, Michael Fosmire, Alexander A. Gurshtein, Marvin Bolt, Suzanne Débarbat, Marilyn Bailey Ogilvie, Gyula Klima, Mary Croarken, Kevin J. Kilburn, Y. Tzvi Langermann, Jean‐Louis Trudel, Dorrit Hoffleit, Thomas A. Dobbins, Grant Christie, Raymond E. White, Peter Broughton, Robert J. Hurry, Roger Cayrel, Joseph F. MacDonnell, Jacques Lévy, Daniel Kolak, Ian Elliott, Thomas J. Bogdan, Yuri V. Balashov, Steven Turner, Alastair G. Gunn, Kristian Peder Moesgaard, Alistair Kwan, Julio Samsó, Wolfgang Kokott, Françoise Launay, Graham Hall, Julian Holland, Alex Dalgarno, Gary L. Cameron, Ian T. Durham, Hartmut Frommert, Davide Neri, Craig B. Waff, Solange Grillot, Edward Baron, Matthew F. Dowd, Y. P. Varshni, Raghini S. Suresh, Audouin Dollfus, Jan Mietelski, Glenn A. Walsh, Robert McGown, Stephen Gaukroger, Voula Saridakis, Alv Egeland, Takanori Kusuba, Josep Casulleras, Antonio Ten, Robert K. DeKosky, Jordan D. Marché, John Hearnshaw, Alan H. Batten, Robert Alan Hatch, Virginia Trimble, William Sheehan, Eugene F. Milone, Gerald P. Verbrugghe, Alan W. Hirshfeld, Steven N. Shore, Roy H. Garstang, Patricia S. Whitesell, Dennis Danielson, Raymonde Barthalot, Peter Wlasuk, Ednilson Oliveira, Robert D. McGown, Oliver Knill, Hidemi Takahashi, Richard A. Jarrell, Richard Baum, Guenther Görz, Jean‐Pierre Luminet, Behnaz Hashemipour, Christian Nitschelm, Paul Couteau, Helmut A. Abt, Martin Solc, Jeff Suzuki, Gustav Holmberg, Michio Yano, Monique Gros, Keith Snedegar, James M. Lattis, Benno van Dalen, Patrick A. Catt, and Thomas R. Williams
- Published
- 2014
13. Bar Ḥiyya: Abraham Bar Ḥiyya Savasorda
- Author
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Josep Casulleras, Thomas J. Bogdan, Takanori Kusuba, William Sheehan, Richard A. Jarrell, Richard Baum, Kristian Peder Moesgaard, Kevin J. Kilburn, Y. Tzvi Langermann, Audouin Dollfus, Peter Broughton, Wolfgang Kokott, Jean‐Pierre Luminet, Dorrit Hoffleit, Jordan D. Marché, Robert Alan Hatch, Voula Saridakis, Alistair Kwan, Grant Christie, Guenther Görz, Yuri V. Balashov, Alv Egeland, Christian Nitschelm, Marvin Bolt, Alex Dalgarno, Robert J. Hurry, Gerald P. Verbrugghe, Mary Croarken, Jeff Suzuki, Steven N. Shore, Suzanne Débarbat, Thomas A. Dobbins, Raymond E. White, John Hearnshaw, Behnaz Hashemipour, Robert McGown, Graham Hall, Edward Baron, Michio Yano, Daniel Kolak, Paul Couteau, Stephen Gaukroger, Matthew F. Dowd, Monique Gros, James M. Lattis, Ronald Florence, Michael Fosmire, Marilyn Bailey Ogilvie, Roger Cayrel, Joseph F. MacDonnell, Ian Elliott, Keith Snedegar, Virginia Trimble, Jürgen Hamel, Oliver Knill, Hidemi Takahashi, Gustav Holmberg, Roy H. Garstang, Dennis Danielson, Benno van Dalen, Alan W. Hirshfeld, Julian Holland, Y. P. Varshni, Alexander A. Gurshtein, Patrick A. Catt, Thomas R. Williams, Peter Wlasuk, Eugene F. Milone, Ian T. Durham, Hartmut Frommert, Jean‐Louis Trudel, Gyula Klima, Craig B. Waff, Julio Samsó, Alastair G. Gunn, Françoise Launay, Alan H. Batten, Gary L. Cameron, Jacques Lévy, Davide Neri, Solange Grillot, Antonio Ten, Robert K. DeKosky, Patricia S. Whitesell, Raymonde Barthalot, Ednilson Oliveira, Robert D. McGown, Jan Mietelski, Helmut A. Abt, Glenn A. Walsh, Martin Solc, Steven Turner, and Raghini S. Suresh
- Subjects
Bar (music) ,media_common.quotation_subject ,Geometry ,Art ,media_common - Published
- 2014
14. Banachiewicz, Thaddeus Julian
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Thomas R. Williams, Steven Turner, Ronald Florence, Michael Fosmire, Alan H. Batten, Jean‐Louis Trudel, Kevin J. Kilburn, Y. Tzvi Langermann, Dorrit Hoffleit, Raymond E. White, Roger Cayrel, Joseph F. MacDonnell, Ian Elliott, Kristian Peder Moesgaard, Gyula Klima, Behnaz Hashemipour, Yuri V. Balashov, Wolfgang Kokott, Jan Mietelski, Paul Couteau, Glenn A. Walsh, Alex Dalgarno, Peter Wlasuk, Craig B. Waff, Robert J. Hurry, Marvin Bolt, Antonio Ten, Robert K. DeKosky, Edward Baron, Matthew F. Dowd, Gerald P. Verbrugghe, Alastair G. Gunn, Françoise Launay, Patrick A. Catt, Jordan D. Marché, Jacques Lévy, Graham Hall, Gustav Holmberg, Jeff Suzuki, Robert Alan Hatch, Martin Solc, Y. P. Varshni, Gary L. Cameron, Eugene F. Milone, Robert D. McGown, Julian Holland, John Hearnshaw, Helmut A. Abt, Ian T. Durham, Hartmut Frommert, Julio Samsó, James M. Lattis, Raghini S. Suresh, Benno van Dalen, Michio Yano, Richard A. Jarrell, Richard Baum, Monique Gros, Keith Snedegar, Audouin Dollfus, Jean‐Pierre Luminet, Oliver Knill, Hidemi Takahashi, Voula Saridakis, Takanori Kusuba, Alv Egeland, Roy H. Garstang, Dennis Danielson, Thomas J. Bogdan, Jürgen Hamel, Josep Casulleras, Patricia S. Whitesell, Alexander A. Gurshtein, Raymonde Barthalot, Ednilson Oliveira, Steven N. Shore, William Sheehan, Guenther Görz, Christian Nitschelm, Virginia Trimble, Alan W. Hirshfeld, Thomas A. Dobbins, Daniel Kolak, Suzanne Débarbat, Robert McGown, Stephen Gaukroger, Marilyn Bailey Ogilvie, Grant Christie, Peter Broughton, Alistair Kwan, Mary Croarken, Davide Neri, and Solange Grillot
- Subjects
Philosophy - Published
- 2014
15. Birjandi: ҁAbd al- ҁAlī ibn Muḥammad ibn Ḥusayn al-Birjandi
- Author
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Patricia S. Whitesell, Raymonde Barthalot, Ednilson Oliveira, Edward Baron, Matthew F. Dowd, Martin Solc, Eugene F. Milone, Josep Casulleras, Kristian Peder Moesgaard, Jordan D. Marché, Marvin Bolt, William Sheehan, Guenther Görz, Peter Wlasuk, Christian Nitschelm, Robert Alan Hatch, Wolfgang Kokott, James M. Lattis, Steven N. Shore, Raymond E. White, Peter Broughton, Ronald Florence, Michael Fosmire, Roger Cayrel, Joseph F. MacDonnell, Alastair G. Gunn, Françoise Launay, Ian Elliott, Benno van Dalen, Alistair Kwan, Alan H. Batten, Thomas A. Dobbins, Gyula Klima, Mary Croarken, Jan Mietelski, Daniel Kolak, Virginia Trimble, Gerald P. Verbrugghe, Oliver Knill, Hidemi Takahashi, Glenn A. Walsh, Patrick A. Catt, Julio Samsó, Alan W. Hirshfeld, Richard A. Jarrell, Richard Baum, Robert J. Hurry, Thomas J. Bogdan, Jean‐Pierre Luminet, Julian Holland, Behnaz Hashemipour, Craig B. Waff, Gary L. Cameron, Kevin J. Kilburn, Y. Tzvi Langermann, Paul Couteau, Robert McGown, Antonio Ten, Robert K. DeKosky, Thomas R. Williams, Stephen Gaukroger, Robert D. McGown, Gustav Holmberg, Jacques Lévy, Ian T. Durham, Dorrit Hoffleit, Grant Christie, Hartmut Frommert, Steven Turner, Raghini S. Suresh, Davide Neri, Jean‐Louis Trudel, Takanori Kusuba, Helmut A. Abt, Yuri V. Balashov, Solange Grillot, Michio Yano, Monique Gros, Keith Snedegar, Y. P. Varshni, Jeff Suzuki, Graham Hall, Jürgen Hamel, Alexander A. Gurshtein, Audouin Dollfus, Suzanne Débarbat, Voula Saridakis, Alv Egeland, Marilyn Bailey Ogilvie, Roy H. Garstang, Dennis Danielson, John Hearnshaw, and Alex Dalgarno
- Subjects
Philosophy - Published
- 2014
16. Endohedral vibrations of Na+ and K+ in C60
- Author
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Y. P. Varshni
- Subjects
Materials science ,Fullerene ,Condensed Matter Physics ,Potential energy ,Spectral line ,Electronic, Optical and Magnetic Materials ,Schrödinger equation ,Ion ,Metal ,symbols.namesake ,Self-energy ,visual_art ,symbols ,visual_art.visual_art_medium ,Electrical and Electronic Engineering ,Atomic physics ,Morse potential - Abstract
In certain endohedral systems a metallic ion is trapped inside C 60 such that the energy minimum corresponds to an off-centre position of the ion. A simple analytical function is proposed to represent the potential–energy curve for such systems. The applicability of this function to potential energy curves of endohedral Na + and Li + ions in C 60 is demonstrated and it is then used to calculate the structure of spectra for the two systems.
- Published
- 2001
17. Trions in CuCl, CuBr and CuI
- Author
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Y. P. Varshni
- Subjects
Self-energy ,Chemistry ,Chemical physics ,Exciton ,Inorganic chemistry ,Bound state ,Trion ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Morse potential - Abstract
A model is proposed for positive trions (X + 2 ) in bulk solids and another one for surface trions. These models are applied to calculate the bound-state eigenenergies for such trions in CuCI, CuBr and CuI.
- Published
- 2001
18. Relation between the energy levels of an electron bound in a screened Coulomb potential
- Author
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Y P Varshni
- Subjects
Physics ,Nuclear Energy and Engineering ,Bound state ,Function (mathematics) ,Electron ,Electric potential ,Plasma ,Partition function (mathematics) ,Atomic physics ,Condensed Matter Physics ,Quantum number ,Parametric statistics - Abstract
Two parametric relations are proposed for calculating the level energies of an electron bound in a screened Coulomb potential in a plasma. The first relation is between the energies of levels which have the same l quantum number. The second relation is able to represent the bound-state energies for 1s, 2p, 3d...levels as a function of the screening parameter to a good degree of accuracy. These two relations taken together can give the energies of any level up to and including n = 8, and estimated energies for n = 9 and 10 for any value of ne and Te. These are relevant for at least three topics in plasma physics. The application of these relations for the calculation of the partition function of plasmas is discussed.
- Published
- 2001
19. Excited States of Biexcitons
- Author
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Y. P. Varshni
- Subjects
symbols.namesake ,Chemistry ,Excited state ,Bound state ,symbols ,Atomic physics ,Condensed Matter Physics ,Biexciton ,Electronic, Optical and Magnetic Materials ,Morse potential ,Schrödinger equation - Published
- 2001
20. WKB quantization rules for three-dimensional confinement
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Y. P. Varshni, Anjana Sinha, and Rajkumar Roychoudhury
- Subjects
Physics ,Work (thermodynamics) ,Quantization (physics) ,Classical mechanics ,Quantum mechanics ,General Physics and Astronomy ,Hydrogen atom ,Radius ,Quantum ,Harmonic oscillator ,WKB approximation - Abstract
Confined quantum systems have been studied by various authors over the past decades, by using various mathematical techniques. In this work, we derive the WKB quantization rules for quantum systems confined in an impenetrable spherical box of radius r0. We apply the proposed method to two systems explicitly, viz., the confined harmonic oscillator and the confined hydrogen atom. The results are found to be in reasonable agreement with those obtained by other methods. PACS No.: 03.65
- Published
- 2001
21. Shifted 1/N expansion for confined quantum systems
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Y. P. Varshni, Anjana Sinha, and Rajkumar Roychoudhury
- Subjects
Physics ,Mechanical system ,Quantum mechanics ,General Physics and Astronomy ,1/N expansion ,Quantum - Abstract
In this paper we formulate the shifted 1/N expansion method for constrained quantum mechanical systems with spherically symmetric potentials. As an example, we apply our technique to the confined Hulthén potential V(r) = Zδ[e -δr/(1 e-δr)] for different values of the confinement parameter b and the screening parameter δ. It is found that the agreement between our results and the exact numerical values is reasonably good.PACS No.: 03.65Ge
- Published
- 2000
22. Critical cage radii for a confined hydrogen atom
- Author
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Y P Varshni
- Subjects
Empirical equations ,Surface (mathematics) ,Physics ,Bound state ,State (functional analysis) ,Function (mathematics) ,Hydrogen atom ,Radius ,Atomic physics ,Condensed Matter Physics ,Cage ,Atomic and Molecular Physics, and Optics - Abstract
A hydrogen atom confined in a spherical box with impenetrable surface is investigated. The critical cage radius , at which a state is no longer bound is calculated for levels up to and including n = 10. Regularities present in these radii are pointed out. An empirical equation is proposed between and n for a fixed . The total number of bound states is also studied as a function of .
- Published
- 1998
23. MAF solution for bounded potential problems
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A K Ghatak, I.C. Goyal, R. Jindal, and Y P Varshni
- Subjects
Physics ,Airy function ,Bounded function ,Quartic function ,Mathematical analysis ,Quantitative Biology::Populations and Evolution ,General Physics and Astronomy ,Perturbation (astronomy) ,Harmonic potential ,Eigenfunction ,Eigenvalues and eigenvectors - Abstract
We present here the solutions of a bounded linear harmonic potential and abounded quartic potential using the modified Airy function (MAF) method. Resultsobtained by the MAF method have been compared with the analytical (numerical)results and with those obtained by the JWKB method. The comparison showsthat the MAF method gives very accurate results and is, in general, the moreaccurate of the two methods. The MAF method also gives an accurate descriptionof the eigenfunction. A perturbation correction when applied to MAF helps usto get very accurate eigenvalues. The method should be useful in determiningthe eigenvalues and the eigenfunctions of any smoothly varying arbitrarypotential confined by infinite walls.PACS No. 03.65
- Published
- 1998
24. Exact solution for the ground state of a confined potential
- Author
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Y P Varshni
- Subjects
Physics ,Constraint (information theory) ,Exact solutions in general relativity ,General Physics and Astronomy ,Function (mathematics) ,Ground state ,Mathematical physics ,Ansatz - Abstract
An Ansatz for the wave function is used to obtain an exact solution for the ground-state energy for the potential T Eo '@o n Ko n So in an impenetrable spherical box, provided a certain constraint is satisfied between the potential parameters, @cKc and S. Two types of solution are shown to exist. Results are obtained for several sets of potential parameters. R´ esum´ e :L 'utilisation un succedane pour la fonction d'onde permet d'obtenir l'energie exacte du fondamental du potentiel T Eo '@o 2n Ko 3 en So dans une boite spherique impenetrable, a condition que certaines contraintes soient satisfaites entre les parametres @cK et S du potentiel. Deux types de solution existent. Nous presentons les resultats pour differents choix de ces parametres. (Traduit par la r ´
- Published
- 1997
25. Quasi-classical investigation of nonpolynomial central potentials with broken supersymmetry
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Pinaki Roy, Georg Junker, and Y P Varshni
- Subjects
Physics ,General Physics and Astronomy ,Supersymmetry ,WKB approximation ,Numerical integration ,Mathematical physics - Abstract
We evaluate energy eigenvalues corresponding to different central potentials with nonpolynomial character and exhibiting broken supersymmetry. The calculations were carried out using numerical integration, the WKB rule, and a quasi-classical quantization rule for broken supersymmetry. It is shown that in most cases the quasi-classical rule gives far better estimates than the WKB rule applied separately to the supersymmetry partners. R´ esum´ e : Nous calculons les valeurs propres d'un Hamiltonien avec potentiel central de type non-polynomial et capable de briser la supersymetrie. Trois methodes sont utilisees: l'integration numerique, la methode WKB et une regle quasi-classique de quantification adaptee aux cas de bris de supersymetrie. Nous trouvons que dans la plupart des cas, la methode semi-classique donne de bien meilleurs resultats que la methode WKB appliquee separement aux partenaires supersymetriques. (Traduit par la r ´
- Published
- 1997
26. Accurate wavefunctions for the confined hydrogen atom at high pressures
- Author
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Y P Varshni
- Subjects
Physics ,Positive energy ,Atom (order theory) ,Physics::Atomic Physics ,Hydrogen atom ,Atomic physics ,Condensed Matter Physics ,Wave function ,Atomic and Molecular Physics, and Optics ,Compressed hydrogen - Abstract
Wavefunctions are proposed for the 1s, 2p and 3d states of the compressed hydrogen atom at high pressures. It is shown that these wavefunctions give highly accurate energies in the positive energy region.
- Published
- 1997
27. Modified shifted 1/N expansion for relativistic Yukawa and Hulthen potentials
- Author
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Y. P. Varshni, Swati Panchanan, and Rajkumar Roychoudhury
- Subjects
Physics ,symbols.namesake ,Dirac equation ,Yukawa potential ,symbols ,General Physics and Astronomy ,1/N expansion ,Mathematical physics - Abstract
The shifted 1/N expansion technique is applied to the radial Dirac equation. It is shown that the fixing condition E1 = 0 produces an enhanced accuracy for Yukawa and Hulthen potentials. The modified shifted 1/N expansion results are compared with the exact numerical results and results obtained by other approximate methods.
- Published
- 1996
28. Supersymmetric modified Airy-function method and its application to the Schrödinger potential V(x) = x6 − 3x2
- Author
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Y. P. Varshni, Rajkumar Roychoudhury, and Anjana Sinha
- Subjects
Physics ,symbols.namesake ,Airy function ,symbols ,General Physics and Astronomy ,WKB approximation ,Eigenvalues and eigenvectors ,Schrödinger's cat ,Mathematical physics - Abstract
A supersymmetric version of the modified Airy-function method is developed. Explicit calculations for eigenvalues are obtained for the Schrödinger potential V(x) = x6 − 3x2. Comparison is made with exact numerical results as well as those of the Wentzel–Kramers–Brillouin (WKB), supersymmetric WKB (SWKB), and modified Airy-function approximation methods.
- Published
- 1996
29. Exact solutions for the potential V(r) = r2 + β/r4 + λ/r6 by supersymmetric quantum mechanics
- Author
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Nivedita Nag, Rajkumar Roychoudhury, and Y. P. Varshni
- Subjects
Physics ,Constraint (information theory) ,Quantum mechanics ,General Physics and Astronomy ,Supersymmetric quantum mechanics - Abstract
A method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r) = r2 + β/r4 + λ/r6, where β and λ are parameters, provided a certain constraint is satisfied between β and λ. Detailed results are given for the ground state as well as for several excited states. A method for determining the exact energies of two levels for the same values of β and λ is given and illustrated by examples.
- Published
- 1995
30. 1/η expansion for the binding energies of finite-depth potentials
- Author
-
M. Bag, Ranabir Dutt, M M Panja, and Y. P. Varshni
- Subjects
Lennard-Jones potential ,Chemistry ,Quantum mechanics ,Binding energy ,General Physics and Astronomy ,Perturbation theory (quantum mechanics) ,Physical and Theoretical Chemistry ,Atomic physics ,Asymptotic expansion ,Diatomic molecule ,Convergent series ,Morse potential ,Dimensionless quantity - Abstract
We present a systematic perturbative method for calculating the binding energies of ro-vibrational quantum states for a finite depth potential. Using an asymptotic expansion in powers of 1/η, where η is the dimensionless physical depth parameter, explicit calculations are performed. Our analytic results lead to highly convergent series for the binding energies, and numerical results for realistic potentials such as Morse and Lennard-Jones potentials are found to be in excellent agreement with the exact ones.
- Published
- 1994
31. TWO ANYONS IN A CONSTANT MAGNETIC FIELD: A NONPERTURBATIVE APPROACH
- Author
-
Barnana Roy, Pinaki Roy, and Y. P. Varshni
- Subjects
Physics ,High Energy Physics::Theory ,Exact results ,Quantum mechanics ,Quantum electrodynamics ,Statistical and Nonlinear Physics ,Supersymmetry ,Condensed Matter Physics ,Constant (mathematics) ,Topological quantum computer ,Coulomb repulsion ,Energy (signal processing) ,Magnetic field - Abstract
Using two nonperturbative methods, namely, the shifted 1/N expansion and the SWKB techniques, we determine the energy levels of a system of two anyons in an external constant magnetic field and interacting via a Coulomb repulsion. Some exact results have also been found using the notion of supersymmetry.
- Published
- 1994
32. WKB approximation for the rotating Morse oscillator
- Author
-
Y. P. Varshni
- Subjects
Physics ,Self-energy ,law ,Quantum mechanics ,Hydrogen molecule ,General Physics and Astronomy ,Morse code ,Ground state ,Diatomic molecule ,Rotation (mathematics) ,WKB approximation ,law.invention ,Morse potential - Abstract
The WKB approximation is applied to the rotating Morse oscillator. Results are presented for the ground state of the H2 molecule and are compared with those obtained by several other methods. The WKB method gives the best results for v > 5. At smaller values of v, the WKB results are only slightly less accurate than the best ones.
- Published
- 1993
33. Relative convergences of the WKB and SWKB approximations
- Author
-
Y P Varshni
- Subjects
General Physics and Astronomy ,Statistical and Nonlinear Physics ,Supersymmetry ,Quantum number ,WKB approximation ,Numerical integration ,Schrödinger equation ,symbols.namesake ,Quantum mechanics ,Convergence (routing) ,symbols ,Mathematical Physics ,Eigenvalues and eigenvectors ,Mathematics ,Mathematical physics - Abstract
The relative convergences of the WKB and SWKB approximations are examined by calculating the eigenenergies for four potentials by one- and two-term WKB and SWKB approximations. Exact eigenenergies for these four potentials are also calculated by a numerical integration of the Schrodinger equation. Varied results are found for the four potentials. It is found that in general the effect of the second term in the WKB and SWKB approximations depends on the potential, the parameters involved and the quantum number of the state. No simple generalizations are possible.
- Published
- 1992
34. Semi-Classical Approximations for the Energy Levels of a Two-Term Inverse Power Potential
- Author
-
Y. P. Varshni
- Subjects
Analytic continuation ,General Physics and Astronomy ,Applied mathematics ,Inverse ,Energy (signal processing) ,WKB approximation ,Expression (mathematics) ,Mathematics ,Power (physics) ,Term (time) - Abstract
By combining the analytic continuation of 1/N results with additional selection criteria implied by the related WKB description, Papp has obtained a closed analytical expression for the energy levels of the following potential: V(r) = De[(re/r)4 - 2(re/r)2]. The eigenenergies obtained from Papp's expressions are compared with those obtained from one-, two-, and three-term WKB approximations. The WKB approximations give better results than Papp's expression but no closed analytical expression can be obtained from them.
- Published
- 1992
35. Application of the shifted large‐N method to the rovibrational spectroscopy of diatomic molecules
- Author
-
R Dutt, M. Bag, Y. P. Varshni, and M M Panja
- Subjects
Chemistry ,General Physics and Astronomy ,Semiclassical physics ,Expectation value ,Rotational–vibrational spectroscopy ,Quantum number ,Diatomic molecule ,Numerical integration ,symbols.namesake ,Franck–Condon principle ,symbols ,Physics::Chemical Physics ,Physical and Theoretical Chemistry ,Atomic physics ,Spectroscopy - Abstract
Computations of energy levels, expectation values of various powers of internuclear separation, and Franck–Condon factors for molecular potentials have been carried out within the framework of shifted large‐N technique. In contrast to other perturbative as well as semiclassical calculations, we obtain compact analytic expressions for these quantities. For illustration, our predicted results for perturbed Kratzer potential are compared with those derived by numerical integration. The method gives quite accurate results for a wide range of rovibrational quantum numbers. Further possible applications, in particular, to Morse oscillators are finally discussed.
- Published
- 1991
36. ON QUASI-EXACTLY SOLVABLE PROBLEMS AND SUPERSYMMETRY
- Author
-
Pinaki Roy and Y. P. Varshni
- Subjects
Physics ,Nuclear and High Energy Physics ,General Physics and Astronomy ,Superstring theory ,Astronomy and Astrophysics ,Supersymmetry ,String (physics) ,Fundamental interaction ,Theoretical physics ,N = 4 supersymmetric Yang–Mills theory ,Quantum mechanics ,Quantum gravity ,Supersymmetric quantum mechanics ,Quantum field theory - Abstract
We discuss the possibility of obtaining new quasi-exactly solvable systems within the framework of supersymmetric quantum mechanics.
- Published
- 1991
37. Family of exact solutions for the Coulomb potential perturbed by a polynomial inr
- Author
-
Rajkumar Roychoudhury, Y. P. Varshni, and Manasi Sengupta
- Subjects
Physics ,symbols.namesake ,Coulomb wave function ,symbols ,Supersymmetric quantum mechanics ,Electric potential ,1/N expansion ,Hamiltonian (quantum mechanics) ,Atomic and Molecular Physics, and Optics ,Eigenvalues and eigenvectors ,Mathematical physics - Abstract
A method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r)=\ensuremath{\alpha}/r+${\mathit{p}}_{1}$r+${\mathit{p}}_{2}$${\mathit{r}}^{2}$+${\mathit{p}}_{3}$${\mathit{r}}^{3}$+${\mathit{p}}_{4}$${\mathit{r}}^{4}$ where \ensuremath{\alpha} and the p's are parameters, provided certain relations are satisfied between the parameters. Detailed results are given for three specific cases. The potential in question gives rise to some very interesting shapes (double-well, etc.). The applicability of the shifted 1/N expansion method to such potential shapes is examined by comparing eigenenergies obtained by this method with the exact ones obtained from supersymmetric considerations. It is found that in certain situations, the shifted 1/N expansion method may give poor or erroneous results. Applicability of the proposed method to potentials involving higher powers of r is also discussed.
- Published
- 1990
38. Shifted large-Nexpansion for a relativistic spin-1/2 particle in screened Coulomb potentials
- Author
-
Y. P. Varshni, M M Panja, and Ranabir Dutt
- Subjects
Physics ,Atomic and Molecular Physics, and Optics ,Relativistic particle ,symbols.namesake ,Pauli exclusion principle ,Quantum electrodynamics ,Dirac equation ,Quantum mechanics ,Bound state ,symbols ,Coulomb ,Wave function ,Spin (physics) ,Klein–Gordon equation - Abstract
The difficulties associated with application of the shifted large-N technique to the Dirac equation have been resolved by applying the method to the Klein-Gordon equation in which a spin-orbit interaction term is included analogous to Pauli theory. Explicit analytical expressions for the relativistic screened Coulomb bound-state energies, radial wave functions, and normalizations are given. For the point-Coulomb problem, we restore exact results for the relativistic binding energies and almost exact wave functions. The 1/N expansion results are then compared with the exact numerical solutions as well as with those obtained in other analytical methods for a number of screened Coulomb potentials and for a wide range of atomic numbers Z. In general, excellent agreement is found. In contrast to the limited applicability of the usual perturbative methods, our technique is found to be flexible and may be extended to a more general class of relativistic potentials that has applications in atomic and quarkonium physics. Encouraging aspects of the present approach are also briefly discussed.
- Published
- 1990
39. Eigenenergies and oscillator strengths for the Hulthén potential
- Author
-
Y. P. Varshni
- Subjects
Physics ,Oscillator strength ,Wave equation ,Atomic and Molecular Physics, and Optics ,Numerical integration ,Schrödinger equation ,symbols.namesake ,Quantum mechanics ,symbols ,Absorption (logic) ,Calculus of variations ,Wave function ,Energy (signal processing) ,Mathematical physics - Abstract
A detailed study of the bound-state properties of the Hulth\'en potential is presented. Accurate eigenenergies are obtained for the Hulth\'en potential by numerical integration of the Schr\"odinger equation. One-parameter variational calculations are carried out. The variational results are practically identical to the exact energies, except in the high-screening region. The critical screening parameter is calculated for various values of l for n\ensuremath{\le}10 by a numerical solution of the wave equation. The energy eigenvalues obtained by a variety of methods are compared and discussed. The variational wave functions are employed to calculate absorption oscillator strengths for 1s\ensuremath{\rightarrow}2p, 1s\ensuremath{\rightarrow}3p, and 2p\ensuremath{\rightarrow}3d transitions.
- Published
- 1990
40. Large-amplitude ion-acoustic double layers in a plasma with warm ions
- Author
-
Y. P. Varshni, Rajkumar Roychoudhury, and Sikha Bhattacharyya
- Subjects
Physics ,General Physics and Astronomy ,Potential method ,Plasma ,Electron ,Charged particle ,Ion ,symbols.namesake ,Amplitude ,Mach number ,Physics::Plasma Physics ,symbols ,Atomic physics ,Magnetohydrodynamics - Abstract
The conditions for the existence of an ion-acoustic double layer in a plasma with warm ions and two distinct groups of hot electrons have been studied using the Sagdeev potential method. A comparison is made with the published results of Bharuthram and Shukla for cold ions and a two-temperature electron population. Numerical studies have been made to find out the effect of a finite ion temperature on the Mach number of the double layers.
- Published
- 1990
41. Weizsäcker, Carl Friedrich von
- Author
-
Y. P. Varshni
- Published
- 2007
42. Bowen, Ira Sprague
- Author
-
Y. P. Varshni
- Published
- 2007
43. Hydrogenic system confined to a two-dimensional circular disc
- Author
-
S H Patil and Y P Varshni
- Subjects
Physics ,States ,Physical structure ,Quantum dot ,Simple (abstract algebra) ,Quantum mechanics ,Quantum Dots ,2 Electrons ,General Physics and Astronomy ,Circular disc ,Wave function - Abstract
Some general properties of a hydrogenic system confined to a circular disc are analyzed. Based on these, simple and accurate expressions are developed for the energies, critical radii, and some other properties, for all the states and all radii of confinement. Model wave functions are considered for some states, which give accurate values for the energies and other properties, and provide an insight into their physical structure. PACS Nos.: 3.65.Ge, 73.21.La, 78.67.Hc
- Published
- 2006
44. Alkali atoms confined to a sphere and to a fullerene cage
- Author
-
Y P Varshni, K. D. Sen, and S H Patil
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Enclosed Quantum-Systems ,Impurity States ,Fullerene ,General Physics and Astronomy ,Compressed Atoms ,Hydrogen atom ,Alkali metal ,Off-Center ,Electron ,Dipole ,Perturbation-Theory ,Energy-Levels ,Polarizability ,Cell Model ,Atom ,Physics::Atomic and Molecular Clusters ,Hydrogen-Atom ,Physics::Atomic Physics ,Atomic physics ,Valence electron ,Ground state ,Normalized Wave-Functions - Abstract
A simple asymptotically correct model potential is considered for the valence electron in an alkali atom. Superposed with the confining infinite barrier potential, this potential yields the energies of various states and the dipole polarizability of the ground state of the confined alkali atom. Superposed with the fullerene shell potential, this potential yields the energies of the alkali atom inside a fullerene cage. Numerical results are presented for Li, Na, K, Rb, and Cs under such confinements. PACS Nos.: 03.65.Ge, 73.21.La, 78.67.Hc
- Published
- 2005
45. Peaks In Emission Lines In The Spectra Of Quasars
- Author
-
Y P Varshni, Talbot, John, and Zhengo Ma
- Published
- 2005
- Full Text
- View/download PDF
46. On the application of supersymmetric WKB (Wentzel–Kramers–Brillouin) method to quasi-exactly solvable problems
- Author
-
P. Roy, Rajkumar Roychoudhury, and Y. P. Varshni
- Subjects
Brillouin zone ,Physics ,Quantization (physics) ,Quantum mechanics ,General Physics and Astronomy ,WKB approximation ,Mathematical physics - Abstract
The WKB (Wentzel–Kramers–Brillouin) as well as the SWKB quantization rules are applied to a number of quasi-exactly solvable problems (which apart from being SU(2) symmetric are also supersymmetric). The results obtained by these methods are compared with the exact numerical results.
- Published
- 1991
47. Modified shifted large-N approach to the Morse oscillator
- Author
-
M. Bag, Ranabir Dutt, Y. P. Varshni, and M M Panja
- Subjects
Physics ,law ,Quantum mechanics ,Bound state ,Eigenfunction ,1/N expansion ,Wave function ,Morse code ,Diatomic molecule ,Atomic and Molecular Physics, and Optics ,Energy (signal processing) ,Eigenvalues and eigenvectors ,law.invention - Abstract
It is observed that the well-known shifted large-N technique proposed by Imbo, Pagnamenta, and Sukhatme [Phys. Rev. D 29, 1669 (1984)] fails to yield the correct behavior of the bound-state wave function for the Morse oscillator. To remove this inadequacy, we propose a modified approach which not only restores the exact analytic expressions for the energy eigenvalues and eigenfunctions for the Morse oscillator but also predicts quite accurate results for the rotating Morse oscillator
- Published
- 1992
48. Large-N expansion method for a spin-1/2 particle in the presence of vector and scalar potentials
- Author
-
M. Bag, Ranabir Dutt, M M Panja, and Y. P. Varshni
- Subjects
Physics ,Classical mechanics ,Scalar (mathematics) ,Bound state ,Coulomb ,Scalar potential ,Wave function ,Vector Laplacian ,Scalar field ,Atomic and Molecular Physics, and Optics ,Vector potential - Abstract
The shifted large-N technique (SLNT) has been applied to study the relativistic motion of a particle in the presence of vector and scalar interactions with special emphasis on the construction of both large- and small-component Dirac radial wave functions. Numerical results for the binding energy for a particle in the presence of the Coulomb plus linear confining potential compare very well with those obtained by the elaborate analytic approximation method using the Pad\'e-approximation technique. We illustrate that one recovers not only the exact analytic results for binding energies for vector and scalar Coulomb potentials, but also exact wave functions from the leading-order SLNT calculation. This motivates future applications of the same method to more realistic atomic systems governed by screened Coulomb potentials where the knowledge of the large and small components of the radial wave function is essential.
- Published
- 1992
49. Conditionally exactly soluble potentials and supersymmetry
- Author
-
Y. P. Varshni, Nivedita Nag, and Rajkumar Roychoudhury
- Subjects
Physics ,Theoretical physics ,Particle physics ,Supersymmetry ,Atomic and Molecular Physics, and Optics - Published
- 1994
50. Effect of dielectric screening on the donor binding energy in silicon and germanium
- Author
-
Y. P. Varshni and S. M. Khanna
- Subjects
Materials science ,Silicon ,chemistry ,Condensed matter physics ,Impurity ,Binding energy ,chemistry.chemical_element ,Shielding effect ,Germanium ,Dielectric ,Thomas–Fermi model ,Ground state - Abstract
L'ecrantage dielectrique lineaire de Thomas-Fermi et ses diverses ameliorations sont utilises pour calculer l'energie de liaison d'un centre donneur dans le silicium et le germanium. Les resultats sont compares aux valeurs experimentales
- Published
- 1991
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