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In this paper, we analyse the quantization of cyclotron orbits for a 2D non-relativistic and spinless charged particle under the influence of a static and uniform magnetic field, the Landau problem. We follow the algebraic approach of rising and lowering operators. The Hamiltonian is expressed in terms of the usual rising and lowering operators of an isotropic quantum oscillator. Through a Bogoliubov transformation, we show that the Hamiltonian may be reduced to the one of a quantum oscillator that accounts for the formation of infinitely degenerate Landau levels. The explicit form of the position-space wave functions of Fock–Darwin states for a vanishing parabolic confinement potential is worked out by applying the techniques of ladder operators and the induction method. To explore the internal dynamics of the electron states, we compute the Fock–Darwin states’ density currents expressing them in terms of the ladder operators. In the supplementary material, we provide the reader with Mathematica algorithm that can help perform some of the calculations exposed in the paper. The charged particle in a magnetic field is used to explore some of the fundamental concepts of quantum mechanics as commuting operators, simultaneous eigenstates, degeneracy, rising and lowering operators, etc. This approach can be used as supplementary material in undergraduate final-year courses like quantum mechanics or solid state physics.

Submitted by Guilherme Lemeszenski (guilherme@nead.unesp.br) on 2013-08-22T18:56:08Z No. of bitstreams: 1 S0102-09352008000500003.pdf: 257919 bytes, checksum: d1422a2702180a82a41cc6fea3d62ec7 (MD5) Made available in DSpace on 2013-08-22T18:56:08Z (GMT). No. of bitstreams: 1 S0102-09352008000500003.pdf: 257919 bytes, checksum: d1422a2702180a82a41cc6fea3d62ec7 (MD5) Previous issue date: 2008-10-01 Made available in DSpace on 2013-09-30T19:49:44Z (GMT). No. of bitstreams: 2 S0102-09352008000500003.pdf: 257919 bytes, checksum: d1422a2702180a82a41cc6fea3d62ec7 (MD5) S0102-09352008000500003.pdf.txt: 24850 bytes, checksum: 1f0cdee8662fba360312abb716584dc9 (MD5) Previous issue date: 2008-10-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T15:13:06Z No. of bitstreams: 2 S0102-09352008000500003.pdf: 257919 bytes, checksum: d1422a2702180a82a41cc6fea3d62ec7 (MD5) S0102-09352008000500003.pdf.txt: 24850 bytes, checksum: 1f0cdee8662fba360312abb716584dc9 (MD5) Made available in DSpace on 2014-05-20T15:13:06Z (GMT). No. of bitstreams: 2 S0102-09352008000500003.pdf: 257919 bytes, checksum: d1422a2702180a82a41cc6fea3d62ec7 (MD5) S0102-09352008000500003.pdf.txt: 24850 bytes, checksum: 1f0cdee8662fba360312abb716584dc9 (MD5) Previous issue date: 2008-10-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Observou-se significativo aumento de atividade das formas ativas das metaloproteinases -2 e -9 em gatos com tirotoxicose induzida e desmineralização óssea. As formas pró e intermediária da metaloproteinase -2 elevaram-se com 14 dias de administração hormonal, porém, posteriormente, houve uma tendência de queda. Observou-se correlação negativa entre a forma ativa das metaloproteinases de matriz -2 e -9 e a densidade mineral óssea da extremidade distal do rádio. Os resultados sugerem aumento da degradação da matriz colágena secundária com a elevação dos hormônios tiroidianos. Significant increase of activity of active forms of matrix metalloproteinases -2 and -9 in cats under induced thyrotoxicosis and bone demineralization was observed. Pro and intermediated forms of matrix metalloproteinases -2 and -9 increased at 14 days of hormonal treatment, followed by decrease tendency. A negative correlation between active forms of matrix metalloproteinases -2 and -9 and bone mineral density of radius distal extremity was also observed. The results suggest an increase of collagen matrix degradation secondary to high levels of thyroid hormones. Universidade Federal do Espírito Santo (UFES) Departamento de Medicina Veterinária UNESPAR FFALM UNESP, Fac Med Vet & Zootecnia, Botucatu, SP, Brazil UNICAMP Instituto de Biologia UNESP Inst Biociencias, Botucatu, SP, Brazil UNESP, Fac Med Vet & Zootecnia, Botucatu, SP, Brazil UNESP Inst Biociencias, Botucatu, SP, Brazil

We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest non-vanishing terms of the wave function near the singularity it is possible to infer the structure of the Bohmian streamlines. Conversely, starting from a map of the electron's Bohmian velocities, we demonstrate that it is possible to derive the form of the electron's wave function near the singularity. We outline a procedure that could yield an experimental method to determine the main parameters of the electron's wave function close to a singularity., Comment: 16 pages, 17 figures, 1 table

We study the spin dynamics of a 2DEG moving across a magnetic superlattice. We describe the spin transitions induced by sectionally homogeneous tilted magnetic fields and the spatial evolution of spin-1/2 wave functions: amplitude and phase, in terms of the tilting angle, the Fermi energy and the magnetic field strengths. Clear signatures of coherent spin mixing and coherent spin flipping processes are shown. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the Shubnikov-de Haas oscillations in the magnetoresistance and Landauer conductance of a three strip quasi-2D semiconductor wave guide with thickness δ z and transversal width Wy. We assume that the strip in the middle, of length l H , is subject to a homogeneous magnetic field, tilted by θ H with respect to the normal z of the 2DEG. The structure of the Shubnikov-de Haas oscillations, associated with spin parallel and antiparallel to the z-component of the magnetic field, and the finiteness of l H , lead us to define, related with the limits between the corresponding Landau levels and the continuous spectrum, two characteristic saturation fields B s a t , đ= 2Φ o /l H cosθ H (2n s π - 1/δ 2 z ) 1 / 2 and B s a t , Đ defined by the positive root of B 2 s a t , Đ + 4gΦ o /πl 2 H cos 2 θ H B s a t , Đ - B 2 s a t , đ= 0. Here g is the Lande factor, Φ o the unit magnetic flux and n s the charge concentration. We also obtain the polarization field B p = Φ 0 /g 2n s - π/δ 2 z .

A phenomenological theory to describe the electromagnetic properties of granular superconductors, based on known bulk superconductors expressions and conventional Josephson's junctions tunneling currents, is presented and succesfully used to fit distinct experimental results for the magnetic susceptibility as a function of the temperature and the applied magnetic field of rather different samples., Comment: 6 pages, 6 figures

Using the transfer matrix method and the multi-channel scattering approach, we solve analytically the Schrodinger equation for spin 12 electrons moving through a homogeneous semiconductor wave guide subject to an external magnetic field, acting on alternating stripes. We study the space-time evolution of Gaussian spin-wave packets inside and outside of the homogeneous magnetic superlattices (MSL) for different tilting angles. We discuss interfering processes of spin-wave packets, defined in the band gap and in the resonant energy regions of homogeneous MSL based on an InSb semiconductor. We show also that the time spent inside the MSL is in good agreement with the phase time predictions.

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. The Green's function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail., Comment: 14 pages, 4 figures, misprints and figures corrected

In this paper we introduce an alternative approach to studying the motion of a planar charged particle subject to a static uniform magnetic field. It is well known that an electric charge under a uniform magnetic field has a planar motion if its initial velocity is perpendicular to the magnetic field. Although some constants of motion (CsM), as the energy and the angular momentum, have been widely discussed for this system, others have been neglected. We find that the angular momentum, the generator of the magnetic translations and the magnetic Laplace–Runge–Lenz vector are CsM for this particular system. We show also that these three quantities form an orthogonal basis of vectors. The present work addresses many aspects of the motion of a charged particle in a magnetic field that should be useful for students and tutors of the classical mechanics courses at the senior undergraduate level.

Using the exact two-propagating-modes solutions for electrons in a quasi-2D semiconductor wave guide under sectionally constant magnetic fields and spin-orbit interactions, it is explicitly shown that the Fano-like resonances and antiresonances lead to sudden suppressions and enhancements of the spin-dependent transmission probabilities. Our calculations show that when the magnetic-field-tilting angle θH is increased, the spin-field interaction becomes the most significant mechanism for the spin transitions in magnetic superlattices. Taking advantage of these spin-transport effects, simple and efficient spin-inverter devices are proposed. To better visualize the relative influence of the specific semiconductor properties on the device performance and device characteristics, we consider two magnetic superlattices based on semiconductors having entirely different Lande g-factor: GaAs and InSb. Although slightly more efficient spin-inversion devices are obtained for the GaAs semiconductor, InSb requires lower magnetic fields and its efficiency can be close to 80%.

Cosmic‐ray‐induced unclear interactions are observed by emulsion chambers exposed on Mt. chacaltaya, Bolivia (5220m above sea level). We detect photons from nuclear interactions which occurred within the petroleum putch layer (1/3 nuclear mean free path), set 150 cm above the emulsion chamber.Photons of energy ≳100 GeV are detected in each event, the highest detected photon energy being 40TeV. 350 events are found to contain 4 or more photons, whose energy sums, ? Eγ, range from 5 TeV up to 500 TeV, and are adopted for analysis.Multiplicity‐, energy‐, angular‐, PT‐, and other related distributions of the photons are presented, comparison is made with the accelerator data, and discussions are given.

Events of a new type have been observed by the chacaltaya Emulsion Chamber Experiment,1,2 which can consistently be interpreted as ’’baryon’’ pair decay of a heavy intermetiate state of rest mas 20–30 GeV/c2.

Centauro‐type and Mini‐Centauro‐type events are reported and discussed. They are events in which nuclear‐active particles (i.e. hadrons which do not undergo rapid photon decays) are produced without any sign of accompanying neutral pion emission. Estimated hadron multiplicity is ∠100 for Centauro‐type and ∠15 for Mini‐Centauro‐type.Up to the present moment, 5 examples of Centauro and 13 of Mini‐Centauro have been observed in the two‐storey emulsion chambers exposed on Mt. Chacaltaya, Bolivia (5220 m above sea level).The experimental results on energy and angular distributions are in agreement with the hypothesis that this type of events occur through production and decay of a fire‐ball with a rest energy of (200∠300) GeV/c2 for Centauro and ∠30 GeV/c2 for Mini‐Centauro events.