Oscillator Wave Functions Research Articles

Temperature and magnetic field dependence of radiation‐induced magnetoresistance oscillations in a 2D electron gas

AbstractA theoretical model is presented in which the existence of radiation‐induced zero‐resistance states is analyzed. An exact solution for the harmonic oscillator wave function in the presence of radiation, and a perturbation treatment for elastic scattering due to randomly distributed charged impurities, form the foundations of our model. Following this model most experimental results are reproduced. The existence of zero‐resistance states is thus explained in terms of the interplay of the electron MW‐driven orbit dynamics and the Pauli exclusion principle. In order to explain the strong temperature dependence of the longitudinal resistivity and the thermally activated transport in 2DEG, we present also a model based on the damping suffered by the microwave‐driven electronic orbit dynamics by interactions with the lattice ions yielding acoustic phonons. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Linear Combination of Vibrational Wave Functions (LCVW) Method in a Morse–Gaussian Double Well Molecular Potential

The linear combinations of harmonic oscillator wave functions (LCWV) method is proposed to solve the Schrodinger equation, for a particle of a mass μ moving in a one dimensional double-well potential field, in which, the energy barrier has a gaussian shape. The general double well potential, whether symmetric or not, is constructed from appropriate combinations of Morse-like potentials and a Gaussian function and the problem is solved variationally, using as trial functions, linear combinations of harmonic oscillator wave functions (LCWV) centered at the two minima. The relevant matrix elements are calculated using the Harmonic Oscillator Tensor (HOT) technique. A generalization to multiple well problems is also advanced.

Higher charmonia

This paper gives results for the spectrum, all allowed E1 radiative partial widths (and some important M1 widths) and all open-charm strong decay amplitudes of all 40 $c\overline{c}$ states expected up to the mass of the $4\mathrm{S}$ multiplet, just above 4.4 GeV. The spectrum and radiative widths are evaluated using two models, the relativized Godfrey-Isgur model and a nonrelativistic potential model. The electromagnetic transitions are evaluated using Coulomb plus linear plus smeared hyperfine wave functions, both in a nonrelativistic potential model and in the Godfrey-Isgur model. The open-flavor strong decay amplitudes are determined assuming harmonic oscillator wave functions and the ${^{3}\mathrm{P}}_{0}$ decay model. This work is intended to motivate future experimental studies of higher-mass charmonia, and may be useful for the analysis of high-statistics data sets to be accumulated by the BES, CLEO, and GSI facilities.

Field effect on optical recombination in Si/SiGe quantum heterostructures having U, W and M type II potential designs

We report on optoelectronic properties of devices based on Si/Si 1− x Ge x systems. To limit the inherent problems of the type II character and the indirect nature of the bandgap, we propose Si/Si 1− x Ge x strained QW s embedded in relaxed Si 1− y Ge y barriers. The conduction and the valence band present a W-, Usami- or M-like potential profile with a quasi-type I heterostructures. Based on Schrödinger equation, a theoretical analysis is made to calculate electric field dependent interband transitions in the three above-mentioned structures. The thickness and compositions ( x > y) of these heterostructures are computed in order to get: (i) the optimum quantum confinement of electrons and heavy-holes levels; (ii) the optimum out of plane oscillator strength and wave functions overlap; (iii) to satisfy a fundamental emission at a key 1.55 μm wavelength below the absorption gap of the three designed structures. The effect of the applied electric field on quantum levels and oscillator strength is discussed.

Structural, Potential Surface and Vibrational Spectroscopy Studies of Hypophosphorous Acid in the Gas Phase and Chain Conformation. A Theoretical Study

The potential energy surfaces (PES), molecular and vibrational structure of hypophosphours acid (HPA) were investigated by HF, MP2 and DFT-B3LYP level of theory using 6-31G** basis set. In order to approach solid state spectra we optimized mono-, di-, tri-, tetraand penta-mer structures and computed frequencies and intensities of the vibrational modes of VCD and IR. It is found that by increasing the number of HPA molecules in the chain, some of calculated vibrational frequencies approach to the experimental solid state values. The potential energy surfaces of HPA are calculated in a wide range on the plane perpendicular to the P-O bond where the hydrogen can rotate 360 degree through O=P-O-H dihedral angle. A circular valley is found going up and down on the plane, the valley is centered to the continuation of P-O bond. There are two minima at angles ±42.5 to the O=P-O plane giving two mirror conformers and one saddle point in between with a height of 284.87 cm at the angles 0 and a complex barrier with a height of 2089.40 cm at the angle 180 to the same plane. On top of the complex barrier, there is a small well with depth of 15.65 cm. To study the tunneling effect and pathway between the two conformers, the molecule is considered to have C S symmetry and a symmetric double minimum potential energy well with a barrier of 284.87 cm height in the middle. With the constructed potential, the torsional motion of P-O-H (Hindered Rotation) of the monomer, using variation method and harmonic oscillator wave functions is studied and IR frequencies and relative intensities of vibrational modes are calculated. Due to the width of the well and the trigonometric shape of the barrier, tunneling can occur at the ground state

Dipole moments of HDO in highly excited vibrational states measured by Stark induced photofragment quantum beat spectroscopy

We report here a measurement of electric dipole moments in highly vibrationally excited HDO molecules. We use photofragment yield detected quantum beat spectroscopy to determine electric field induced splittings of the J=1 rotational levels of HDO excited with 4, 5, and 8 quanta of vibration in the OH stretching mode. The splittings allow us to deduce mua and mub, the projections of dipole moment onto the molecular rotation inertial axes. We compare the measured HDO dipole moment components with the results of quantitative calculations based on Morse oscillator wave functions and an ab initio dipole moment surface. The vibrational dependence of the dipole moment components reflect both structural and electronic changes in HDO upon vibrational excitation; principally the vibrational dependence of the O-H bond length and bond angle, and the resulting change in orientation of the principal inertial coordinate system. The dipole moment data also provide a sensitive test of theoretical dipole moment and potential energy surfaces, particularly for molecular configurations far from equilibrium.

Microwave-induced zero-resistance states on 2D electron gas: theoretical explanation and temperature dependence

A new theoretical model is presented in which the radiation-induced zero-resistance states and resistivity oscillations are analyzed. The basis of our model is an exact solution for the harmonic oscillator wave function in the presence of radiation and a perturbation treatment for elastic scattering due to randomly distributed charged impurities. Following this model most experimental results are reproduced: zero-resistance states, resistivity oscillations and the dependence of resistivity with temperature, where a physical model of interaction with acoustic phonon is presented, and an activation energy is calculated.

Overtone spectrum of SiH stretching in H 2 SiCl 2

The overtone spectra of H2SiCl2 molecule in the regions of 2000–9000cm −1 and 12000–12900cm −1 at room temperatures have been studied by use of high-resolution Fourier transform spectroscopy and sensitive-intracavity-laser absorption spectroscopy, respectively. The variations of vibrational quantum numbers Δ VSiH =1, 2, 3, 4 and 6 for the overtones of the SiH stretching have been analysed and assigned with the local mode model and the normal mode model. The values of harmonic frequency ωm , anharmonicity constant χm , bond coupling constant λ, the Morse oscillator parameters D e , α and interaction force constant f rr' are derived from the experimental spectrum with nonlinear least-squares fitting. The most striking feature of the SiH2Cl2 is that the larger the vibrational energy, the smaller the energy difference between a couple of lowest stretching states of a given manifold and finally, the couple of lowest stretching states are degenerated within the experimental error for Δ VSiH≥4 vibrational manifolds. The degenerate energy level structure resembles that of a diatomic Morse oscillator; the transition energies show a remarkable fit to the Birge–Sponer relation. The high vibrational states can be described straightforward with a SiH diatomic Morse oscillator wavefunction, this is an indication of vibrational bond localization.

Theoretical Approach to Microwave-Radiation-Induced Zero-Resistance States in 2D Electron Systems

We present a theoretical model in which the existence of radiation-induced zero-resistance states is analyzed. An exact solution for the harmonic oscillator wave function in the presence of radiation, and a perturbation treatment for elastic scattering due to randomly distributed charged impurities, form the foundations of our model. Following this model most experimental results are reproduced, including the formation of resistivity oscillations, their dependence on the intensity and frequency of the radiation, temperature effects, and the locations of the resistivity minima. The existence of zero-resistance states is thus explained in terms of the interplay of the electron microwave-driven orbit dynamics and the Pauli exclusion principle.

Mass quantization in quantum and susy cosmological models with matter content

We present the study of the quantum closed Friedmann-Robertson-Walker (FRW) cosmological model with a matter content given by a perfect fluid with barotropic state equation p = γρ The Wheeler-DeWitt equation is viewed as the Schrödinger equation for the linear harmonic oscillator with energy E. Such type of Universe has quantized masses of the order of the Planck mass and harmonic oscillator wave functions. Then, we consider the n = 2 supersymmetric superfield approach for the same model and obtain a normalizable wave function (at zero energy) of the universe. Besides, the mass parameter spectrum is found in the Schrödinger picture, being similar to those obtained by other methods, using a black hole system.

IS IT POSSIBLE TO CONSTRUCT THE PROTON STRUCTURE FUNCTION BY LORENTZ-BOOSTING THE STATIC QUARK-MODEL WAVE FUNCTION?

The energy-momentum relations for massive and massless particles are E=p2/2m and E=pc respectively. According to Einstein, these two different expressions come from the same formula [Formula: see text]. Quarks and partons are believed to be the same particles, but they have quite different properties. Are they two different manifestations of the same covariant entity as in the case of Einstein's energy-momentum relation? The answer to this question is YES. It is possible to construct harmonic oscillator wave functions which can be Lorentz-boosted. They describe quarks bound together inside hadrons. When they are boosted to an infinite-momentum frame, these wave functions exhibit all the peculiar properties of Feynman's parton picture. This formalism leads to a parton distribution corresponding to the valence quarks, with a good agreement with the experimentally observed distribution.

Wave function engineering in W designed strained-compensated Si/Si1−xGex/Si type II quantum wells for 1.55μm optical properties

During the past decade, ultra-short period Si n Ge m zone-folded superlattices and Ge/Si quantum dots have been investigated as building blocks for potential light emitting devices compatible with the on-chip CMOS technology. The aim of these nanostructures is to overcome the k-space indirect nature of the bandgap. Strangely, few attentions have been paid to the conventional and less sophisticated quantum well (QW) approach for emission. To limit at first the problems inherent to the real space indirect character of the type II interface in this system of material, we propose a Si/Si 1− x Ge x /Si strained double QW embedded in relaxed Si 1− y Ge y barriers. The conduction and the valence bands present a W-like potential profile, resulting in a quasi-type I heterostructure. The thickness and compositions ( x > y ) of this single W-QW are computed in order to get (i) the optimum quantum confinement of single electrons and heavy-holes levels, (ii) the optimum out of plane oscillator strength and wave functions overlap and (iii) the requested fundamental emission at a key 1.55 μm wavelength below the absorption edge of each constitutive materials. Furthermore, the structure is designed in a realistic way for epitaxial growth assuming strain compensation on relaxed Si 1− y Ge y and thickness of each layer being smaller than the known critical thickness.

Demonstration of systematic improvements in application of the variational method to strongly bound potentials

In applying the variational method, six different sets of trial wave functions are used to calculate the ground state and first excited state energies of the strongly bound potentials, i.e. V(x) = x 2 m , where m = 4, 5 and 6. It is shown that accurate results can be obtained from thorough analysis of the asymptotic behaviour of the solutions. Consequently, it was found that there is a progressive qualitative change in the wave functions from the harmonic to anharmonic and then strongly bounded region, which explains why using a harmonic oscillator wave function together with the conventional perturbative approach to calculate the energy correction, was unsuccessful.

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.

Common generating functions of complete harmonic oscillator wave functions and transformation brackets in D dimensions

AbstractThe separability of the Schrödinger equation for harmonic oscillators in D dimensions and in different coordinate systems (Cartesian, circular, spherical) makes possible the construction of common generating functions for the complete harmonic oscillator wave functions in the corresponding dimensions and coordinates. Explicit forms of such generating functions and their series expansions are presented, and one of their applications is illustrated through the evaluation of transformation brackets. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

A Modification of the Projection Operator Method for Resonances

The Projection Operator Method as applied to the study of resonances is first briefly reviewed. Its shortcomings, in the context of reactions that involve forbidden states are mentioned. The forbidden states arise due to the requirement of antisymmetrization imposed by the Pauli exclusion principle, on the many body wave function. A modification that takes into account the forbidden states is suggested. The modified formalism is applied to the alpha-alpha scattering involving realistic interactions. In place of the usual practice of using oscillator wave functions, bound states are extracted from the scattering potential and are used in obtaining the results. The calculated resonance energies, widths and phase shifts, show excellent agreement with experiment. Since forbidden states should be present in almost any nucleus-nucleus interaction the procedure has a wide range of applicability. It is concluded that the modifications are necessary, if agreement with experiment is to be established.

Some further considerations on deriving matrix elements of non-periodic potentials in the basis of the non-degenerate harmonic oscillator wavefunctions

Using the properties of the generating function of the Hermite polynomials, we have calculated the matrix elements for the Gaussian-type potential V G (x)=A exp{−B(x−C) 2} and for the Morse-type potential V M( x)= D e[1−exp(− ax)] 2 in the basis of the non-degenerate harmonic oscillator wavefunctions. The final forms of these matrix elements are very simple to use and hence suitable for the numerical resolution of the Schrödinger equation for multiple-well potentials or anharmonic oscillators.

Visualizing the phonon wave function

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.

Semileptonic (Λ b → Λcev) decay in a field theoretic quark model

The semileptonic decay width of heavy baryons such as (Λ b → Λcev) has been estimated in the framework of a nonrelativistic field theoretic quark model where four component quark field operators along with a harmonic oscillator wave function are used to describe translationally invariant hadronic states. The present estimation does not make an explicit use of heavy quark symmetry and has a reasonable agreement with the experimentally measured decay width, polarisation ratio and form factors with the harmonic oscillator radii and quark momentum distribution inside the hadron as free parameters.

Identification of the (CO2)2 Dimer Vibrations in the ν1, 2ν2 Region: Anharmonic Variational Calculations

This paper aims at examination of the (CO2)2 spectral absorption profile retrieved from the room temperature CO2 collision-induced absorption (CIA) spectrum in the region of the ν1, 2ν2 Fermi doublet. The assignment of (CO2)2 vibrations is discussed, paying due attention to high-resolution CARS observations in the regions of νlow and νup. A variational solution of the anharmonic vibrational problem for the (CO2)2 dimer was obtained using an extended basis set consisting of harmonic and Morse oscillator wave functions. This allowed for a satisfactory description of the vibrational dimer ν1, 2ν2 spectrum from first principles. In particular, we have succeeded in proving that the diffuse absorption band seen in the trough between the major Fermi-coupled CIA bands belongs to combinations of CO2 bending vibrations in a dimer.