Search

For a nonrelativistic particle acted on by a spatially uniform but possibly time-dependent force, or for a harmonic oscillator also subject to such a uniform force, the wave function differs from that without the force only by a spatial displacement and a phase factor. The shifts in position and phase are simply derived from a solution of the classical equations of motion. [c] 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3481703]

Electromagnetic fields in uniaxial anisotropic media can be obtained based on spherical vector wave functions in isotropic media. Applying the boundary conditions of electromagnetic fields on each interface of an impedance sphere coated with a uniaxial anisotropic layer, the expansion coefficients of electromagnetic fields in the uniaxial anisotropic medium and free space can be derived. The present method is very general, which can be reduced to many isotropic subcases. The present method has been validated in those subcases. Scattering by an impedance sphere with an anisotropic coating is presented and discussed. Index Terms--Anisotropy ratio, electromagnetic scattering, impedance sphere, spherical vector wave functions, uniaxial anisotropic media.

In this paper, an incoherent control scheme for accomplishing the state control of a class of quantum systems which have wavefunction-controllable subspaces is proposed. This scheme includes the following two steps: projective measurement on the initial state and learning control in the wavefunction-controllable subspace. The first step probabilistically projects the initial state into the wavefunction-controllable subspace. The probability of success is sensitive to the initial state; however, it can be greatly improved through multiple experiments on several identical initial states even in the case with a small probability of success for an individual measurement. The second step finds a local optimal control sequence via quantum reinforcement learning and drives the controlled system to the objective state through a set of suitable controls. In this strategy, the initial states can be unknown identical states, the quantum measurement is used as an effective control, and the controlled system is not necessarily unitarily controllable. This incoherent control scheme provides an alternative quantum engineering strategy for locally controllable quantum systems. Index Terms--Incoherent control, quantum reinforcement learning (QRL), wavefunction controllability, wavefunction-controllable subspace.

The accurate quantum 3D calculations of highly excited intermolecular vibrational states of the van der Waals (vdW) complexes tetracene.He and pentacene.He are described. The intermolecular potential energy surfaces are corrugated in the direction of the long axis of aromatic molecules due to the presence of the symmetrically equivalent global double minimum for teracene.He and a triple minimum for pentacene.He on each side of the aromatic plane.

Experiments are conducted to show that scanning tunneling spectroscopy (STS) images of semiconductor quantum dots display clear signatures of electron-electron correlation. The wave-function sequence is described in terms of images of one- and two-electron states by comparing measured STS images of freestanding InAs quantum dots with those calculated by the full configuration interaction method.

The Bloch wave formalism is employed to explain the asymmetry of the spectral response of various distributed-feedback lasers with respect to the gap by terminating the laser facets judicially. The analysis proves that the phase and amplitude of the reflection coefficient for Bloch waves are extremely helpful in determining the spectral characteristics of such distributed-feedback lasers.

In this paper, based on the theory of elastic thin plates, applying the image method and the wave function expansion method, multiple scattering of elastic waves and dynamic stress concentration in semi-infinite plates with a circular cutout are investigated, and the general solutions of this problem are obtained. As an example, the numerical results of dynamic stress concentration factors are graphically presented and discussed. Numerical results show that the analytical results of scattered waves and dynamic stress in semi-infinite plates are different from those in infinite plates when the distance ratio b / a is comparatively small. In the region of low frequency and long wavelength, the maximum dynamic stress concentration factors occur on the illuminated side of scattered body with [theta]=[pi] but not on the side of cutout with [theta]=[pi]/2. As the incidence frequency increases (the wavelength becomes short), the dynamic stress on the illuminated side of cutout becomes little, and the dynamic stress on the shadow side becomes great. [DOI: 10.1115/1.2198545]

The spectroscopic parameters for the intermediated of multicopper oxidases (MCOs) are calculated using multireference wave functions from the CASPT2 and MRDDC12 methods. The results have supported the suggestion that the native intermediate (NI) has an [O.sup.2-] atom in the center of the trinuclear cluster, whereas both the peroxy intermediate (PI) and the peroxy adduct (PA) have an [O.sub.2.sup.2-] ion in the center of the cluster, which agrees well with the quantum mechanical/molecular mechanical (QM/MM) results and spectroscopic measurements.

This paper considers the radiation of sound from compact 2-D or 3-D sources located in an otherwise rigid wall, bounding a region of fluid flowing parallel to the wall. The sound radiation problem is modeled using a wave number decomposition. Numerical results show how the radiated power and directivity depend on the freestream flow Mach number and the thickness of the boundary layer adjacent to the wall. The numerical model is validated by comparing the sound power and directivity obtained in the limiting case of a thin boundary layer with that obtained from an alternative analytical model in which the flow is uniform and there is slip at the boundary. DOI: 10.2514/1.19138

We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a condensate wave function with a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state for which the particle number is uncertain, but the phase is known. How such a state would be prepared before an experiment is not obvious. We show that a phase can also arise from experiments using condensates with known particle numbers. The analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of spontaneously broken gauge symmetry and to hidden variables is discussed. [DOI: 10.1119/1.2210489]

A generalized version of the two-dimensional prolate spheroidal wave function (2-D PSWF) theory that can be applied to nonrectilinear magnetic resonance imaging (MRI) data acquisition methods is presented in order to make the method more suitable for dynamic studies. The method is applied to an fMRI study using a spiral trajectory, which illustrates its efficiency at tracking hemodynamic signals with high temporal resolution.

An efficient procedure to compute Hamiltonian matrix elements and reduced one- and two-particle density matrices for electronic wave functions using a new graphical-based nonlinear expansion form is presented. This method is based on spin eigenfunctions using the graphical unitary group approach (GUGA), and the wave function is expanded in a basis of product functions, allowing application to closed- and open-shell systems and to ground and excited electronic states.

Rotationally inelastic scattering of rare gas atoms and oriented NO molecules exhibiting a remarkable alternation in the sign of steric asymmetry between even and odd changes in rotational quantum number are presented. It is observed that the effects are found in full quantum-mechanical scattering calculations.d

Byline: Ramon Carbo-Dorca (1,2) Keywords: Einstein--Podolski--Rosen paradox; wavefunction structure; expectation values; inward matrix product; selectors Abstract: A unique wavefunction, constructed according to the original Einstein--Podolski--Rosen (EPR) description, is used here to analyze the behavior of two equal non-interacting quantum systems: S(1) and S(2).The results show that the EPR paradox, which will be referred as EPR effect in this work, always appears in this theoretical context. When the expectation value of a Hermitian operator is sought, it can yield two different values, when measured on S(1) or S(2). However, the EPR effect disappears if the wavefunction is chosen symmetric or antisymmetric by interchanging the S(1) and S(2) coordinates. The same EPR effect appears when the expectation value of a state selector projection operator is computed on S(1) or S(2), but it disappears within a symmetric or antisymmetric EPR wavefunction form. On the other hand, the action of the selectors over the EPR wavefunction provide images on EPR system S(1) or S(2) which could be different, so the EPR effect persists except if, similarly as in the statistical case, a wavefunction constructed with a symmetric or antisymmetric superposition with respect the EPR system coordinates is used. Thus, with appropriate wavefunction choices, in statistical expectation value measures and non-statistical selector images as well, the EPR effect could not persist. Author Affiliation: (1) Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281, B-9000, Gent, Belgium (2) Institut de Quimica Computacional, Universitat de Girona, Girona, 17071, Catalonia, Spain Article History: Registration Date: 21/10/2005 Received Date: 07/06/2005 Online Date: 23/12/2005 Article note: *This second paper on EPR paradox is also expressly dedicated to the memory Professor Einstein, in order to celebrate the 100th anniversary of the first paper on relativity theory, but also to commemorate the 75 anniversary of the publication of EPR paradox, thus, as before, Professors Podolski and Rosen are also included in the homage.

Charging effects in a CdSe nanotetrapod are theoretically investigated by using an atomistic pseudopotential method. It is found that surface polarization can significantly change the electron wave functions and depending on the situation the tetrapod can behave like a single coherent dot to weakly coupled multiple dots.

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere is formulated and obtained, where the inhomogeneous plasma anisotropic sphere is divided into (s - 1) homogeneous anisotropic spherical layers. The electromagnetic fields in the inner spherical multilayers and outer free space of the inhomogeneous plasma anisotropic spherical structure can be expanded in terms of the spherical vector wave functions in plasma anisotropic medium and in isotropic medium, respectively. By applying the continuous boundary conditions of electromagnetic fields on the spherical interfaces of the (s - 1)-layered homogeneous anisotropic plasma medium, the unknown expansion coefficients of fields in the multilayered plasma spherical structure are obtained, and then the electromagnetic field distributions are calculated. Numerical results for the very general inhomogeneous plasma dielectric material sphere are given and the data in a special case are obtained using the present method and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach and compared to each other to verify the correctness and applicability of the present analysis. Index Terms--Anisotropic media, plasma materials, scattering, wave functions.

A description on a donor center embedded in a thin heterostructural barrier separating a semiconductor medium into two halves is presented. As a result of the small thickness of this barrier, the wave function of an electron bound by the donor center shifts almost completely into both halves of the surrounding semiconductor medium.

A parametric method and a nonparametric method for the identification of traveling flexural vibrations are presented and these methods are complemented by a tuning stage capable of generating traveling waves for a wide range of excitation frequencies. It is observed that the low efficiency, in terms of mechanical response level to electrical input power, is a consequent of inexistence of resonance when pure traveling waves are tuned.

Initial state-specified integral cross section and rate constant for the C(super 1)D +H2 reaction is computed. The calculated initial state-specific constant is shown to be nearly temperature-independent above 100 K.

The hydrogen bonds formed between the hydroperoxyl radical and formic, acetic and trifluoroacetic acids are characterized using geometric, energetic, and electronic parameters through the calculations done with the UB3LYP/6-311++G(3df,3pd) and UB3LYP/EPR-III methods. The wave functions were analyzed through the natural bond orbital, natural steric analysis, natural resonance theory, and atoms in molecules methods.

DFT calculations at the Becke3PW91/6-31+G(d) level of theory provided optimized geometries, transition states, and wave functions suitable for the study of the reactivity and molecular structure with Atoms-in-molecules (AIM) of phosphite ozonide complexes. These calculations also provided activation energies for the extrusion of singlet oxygen from the ozonides, which occurs in a concerted manner. The molecular species investigated were trimethyl phosphite ozonide (1), triphenyl phosphite ozonide (2), trifluoromethyl phosphite ozonide (3), trifluoroethyl phosphite ozonide (4), 4-ethyl-1-phospha-2,6,7-trioxabicyclo[2.2.2]octane ozonide (5), 1-phospha-2,6,7-trioxabicyclo[2.2.2]octane ozonide (6), 1-phospha-2,8,9-trioxadamantane ozonide (7), and propylene phenyl phosphite ozonide (8). Single-point calculations at the Becke3PW91/6-311++G(d,p) level on the geometries obtained from the lower level theory yielded activation energies of 15.1 and 16.4 kcal [mol.sup.-1] for the nonconstrained complexes 1 and 2, respectively. These values differed from the electronegative trifluoro derivatives 3 and 4, which had much higher barriers of 23.5 and 20.8 kcal [mol.sup.-1], respectively. The activation energies of the bicyclic complexes 5-7 were significantly higher than 1 and 2 and comparable to 3 and 4, ranging from 23 to 26 kcal [mol.sup.1]. An intermediate barrier of 20.5 kcal [mol.sup.1] was computed for 8. AIMPAC studies showed no direct correlation between the AIM atomic charges on the phosphorus or oxygen atoms of the ozonide ring with the ease of decomposition of 1-8 to singlet oxygen and the corresponding phosphate. Key words: phosphite ozonide complexes, decomposition, DFT methods, AIM, activation energy.

The study was conducted to describe a hybrid quantum mechanical/molecular mechanical(QM/MM) method implemented in the context of floating-occupation molecular orbital semiempirical configuration interaction wave functions. The effect of solvation on the photochemical energy landscapes of the 150 water molecules was investigated and a tendency for conical intersections to become absolute excited state minima upon hydration was determined.

By using the fast Fourier transform, the spectral and temporal characteristics of multi-mode laser radiation are investigated for different levels of spectral phase coherence. The transition between continuous-wave and mode-locked regimes in lasers is also discussed.

An approach to measure the amount of chirality in the electronic wave function and to apply it to the study of a set of asymmetric aminohydroxylation reactions is reported. A model that evaluates the amount of electronic chirality in a molecular wave functions is presented.

The aim of this brief is to present a modeling procedure for the traveling-wave analog phase shifter. The proposed approach is based on the image representation of two-port networks. Design considerations to optimize the electric performance of the component reducing also the size of the structure are discussed. A commercial software package is used for the final electric simulation of the actual phase shifters to check the validity of the analytic model presented. Index Terms--Image parameters, microwave, phase shifter.

We describe a novel technique for deriving wave-front aberrations from two defocused intensity measurements. The intensity defines a probability density function, and the method is based on the evolution of the cumulative density function of the intensity with light propagation. In one dimension, the problem is easily solved with a histogram specification procedure, with a linear relationship between the wave-front slope and the difference in the abscissas of the histograms. In two dimensions, the method requires use of a Radon transform. Simulation results demonstrate that good reconstructions can be attained down to 100 photons in each detector. In addition, the method is insensitive to scintillation at the aperture. OCIS codes: 010.1080, 010.7350.

This paper presents a numerical method based on finite elements in both frequency and time domain for modeling the coupling of an incident wave with a conducting wire placed inside a metallic cavity having a small aperture. The method uses edge elements on tetrahedra for the electric field representation. The formulation can take into account thin wires as well as lumped elements, in the time-domain approach, the time derivatives are discretized by the Newmark method, which allows obtaining an unconditionally-stable scheme with second-order accuracy. Numerical results are provided to validate the presented method. Index Terms--Aperture coupling, electromagnetic compatibility, enclosure, finite-element methods.

Exact solution of the canonical problem of diffraction of a plane wave by an arbitrarily angled impedance wedge given by Maliuzhinets is employed to derive asymptotic approximations to the field components in a region contiguous to a face of the wedge. The asymptotic solution accounts for terms of order [(k[rho]).sup.-3/2] (k is the wave number and [rho] is the distance from the edge) is uniform with respect to observation and illumination aspects, and includes the case of grazing illumination of a wedge face, which is known to be particularly difficult for the high-frequency analysis (Ufimtsev's singularity). Index Terms--Antenna theory, approximation methods, current distribution, diffraction, geometrical theory of diffraction, impedance, physical theory of diffraction, propagation, surface waves, wedges.

Fatigue is produced by the sum of randomly phased sine waves. Fatigue damage during this non-Gaussian, finite random process is a function of the noise bandwidth, the fatigue slope, mean stress, and the rms stress. Methods are developed for predicting the cycles to failure. Comparison is made with data. [DOI: 10.1115/1.1428332]

Accelerated boundary layers are considered to be stable for practical purposes. It is shown that small suction nonuniformities can induce an instability that results in the generation of streamwise vortices. Addition of a uniform suction is not effective in controlling this instability. It is shown that nonuniformities of surface blowing might induce a similar instability and that the characteristics of this instability are also little affected by the magnitude of the blowing. The same nonuniformities appear to have a small effect on the traveling (Tollmien-Schlichting) wave instability in the range of parameters studied. It is shown that oblique waves become dominant if the amplitudes of the nonuniformities become large enough.

A phase Ronchi grating-based real-time polarization phase-shifting method can be efficiently used for dynamic phase measurement in optical interferometry. A thorough error analysis is required for exhibiting how error sources influence phase-measurement results. We analyze the phase-measurement errors that are induced by the retardation error and azimuth angle error of the quarter-wave plate, the azimuth angle error of polarizers, the phase and intensity aberrations of diffractive wave fronts, and pixel mismatch of the interferometric patterns. The results will also be useful for evaluating the phase-measurement accuracy of other similar systems. OCIS codes: 050.1950, 120.3940, 120.5050.

A method for phase measurement in common-path interferometers, believed to be novel, is presented. We use the property of phase reconstruction algorithms, such as the Carre and Hariharan algorithms, that do not require uniform phase across the reference beam. Only the ratio of the phase steps must be the same at each pixel. We show phase measurement and reconstruction in a common-path interferometer by shifting either the tilt or the focus of the reference wave front. We present a theoretical explanation of phase measurement using this property. We also present results from a proof-of-principle experiment using a scatterplate interferometer, in conjunction with the tilt phase-shifting technique, to measure the reflected phase of a test optical element. Furthermore, we present a computer simulation to demonstrate the mathematical validity of this measurement technique using defocus shifting, rather than tilt shifting, in the reference wave front. OCIS codes: 120.3180, 120.5050, 120.6650, 120.3940.

This paper addresses the question of what happens to a particle in a box that is initially in the ground state, when the box is split into two slightly unequal halves. If the splitting is done sufficiently slowly, it is found that the particle always ends up in the bigger half of the box, regardless of how small the difference in sizes of the two halves may be. Approximate analytical expressions that describe the process are derived, and an optical analogy is presented. [DOI: 10.1119/1.1446854]

A phonon often is described as 'a quantum of lattice vibration,' but this description can be difficult to reconcile with the wave functions explored in a typical undergraduate quantum mechanics class. A phonon wave function is similar to the harmonic oscillator wave functions studied in introductory quantum mechanics, except that it is many-dimensional. We suggest a way to visualize the probability density for this very high-dimensional wave function. The resulting pictures are especially clear and intuitive for a coherent state, which is both a good approximation to a sound wave and a discrete analog to laser light. These pictures can also provide a qualitative introduction to quantum field theory. [DOI: 10.1119/1.1446858]

Byline: V.N. Glushkov (1) Keywords: partially restricted wave function; orthogonality constraints Abstract: An alternative method of building a partially restricted single Slater determinant with the number of [alpha] electrons equal to the number of [beta] electrons has been proposed. Using a simple to implement method of taking the orthogonality constraints into account the amended unrestricted Hartree--Fock (UHF) equations for molecular orbitals have been obtained. The formalism deals as does the UHF theory with the cubic equations with respect to the LCAO coefficients whereas a partially restricted HF approach developed in [10] leads to the fifth-degree equations. The minimal extra calculations are required to implement this scheme in existing UHF codes. Unlike the known Roothaan coupling formalism the proposed approach is suitable for use with the well-established unrestricted Moller--Plesset perturbation theories in incorporating the electron correlation effects. Some peculiarities of using the method are illustrated by considering a model molecular system. Author Affiliation: (1) Physics Department, National University, 49050, per. Nauchny 13, Dniepropetrovsk, Ukraine Article History: Registration Date: 09/10/2004

A study of the three-dimensional wave packet calculations for total momentum quantum number J greater or equal to zero is performed using Jacobi coordinates is presented. The results show that a wave packet representing a rotating triatomic molecule is propagated in Jacobi coordinates for total angular momentum quantum number J equal to 0, 1, and 2.

A study of the effect of adding increasing numbers of the water molecules on several DFT-based reactivity descriptors of ammonia using the effective fragment potential (EFP) model is presented. The study shows that HOMO-LUMO gap and electrphilic hardness are seen to increase with addition of water molecules and the solvent effect on ammonia's properties of wave function relaxation is presented.

Collision-induced and photoinduced electronically diabatic transitions in polyatomic systems are presented, with an eikonal representation of the molecular wave function and developing a self-consistent eikonal approximation for short deBroglie wavelengths. The approach provides state-to-state transition amplitudes for electronic excitation.

The semiclassical wave function for a tunneling electron interacting with the medium is constructed. This wave function permits to describe the evolution of the medium degrees of freedom caused by the tunneling electron.

A vibrational basis representation example and a discrete variable representation example demonstrate that it is possible to use the Lanczos method and exclude direct product basis functions. This is achieved by restricting the basis function indices while maintaining the favorable n(super f+1) scaling relation for the cost of direct product basis matrix-vector products.