Proceedings of the YSU A Physical and Mathematical Sciences

AN ELECTRON ENERGY SPECTRUM AND WAVE FUNCTION IN THE FIELD OF ASYMMETRIC QUANTUM WELL WITH ARBITRARY SHAPE OF THE BOTTOM

Д. М. Седракян, A. Zh. Khachatrian

Published Jul 15, 2002• 0 citations

Abstract

A new method for consideration of an electron stationary motion in the field of an arbitrary one-dimensional potential. It is shown that for a case of an electron infinite motion, the problem of determination of wave functions can be represented as Cauchy problem for the one-dimensional Schrodinger equation. For the case of finite motion the equation determining the energy spectrum is found. It is proved, when the spectrum of bound states is know, the problem of building the wave functions of the discrete spectrum can be formulated as Cauchy problem for wave equation as well.

DOI: 10.46991/pysua.2002.36.2.058

Related papers

Stationary motion of a quantum particle in the field of a one-dimensional arbitrary potential

А. Ж. Хачатрян, Д. М. Седракян, V. A. Khoetsyan

A new approach to the problem of description of the stationary motion of a quantum particle in the field of a one-dimensional arbitrary potential is developed. It is shown that the wave function of infinite motion, with the accuracy to two arbitrary constants, can be expressed by means of an arbitrary single solution for some set of linear differential equations of the first order. It is shown that one general property of the Schrödinger equation solutions lies in the basis of many known methods of the problem consideration, such as the method of integral equations, transfer-matrix method, imbedding method, and method of combination of scattering parameters. Within the framework of the proposed approach, the connection between the above-mentioned methods becomes more transparent.

Journal of Contemporary Physics (Armenian Academy of Sciences)Mar 6, 20094 citations

Stationary motion of a quantum particle in an arbitrary one-dimensional potential

А. Ж. Хачатрян, Д. М. Седракян, V. A. Khoetsyan

A consistent approach to the description of a stationary motion of a quantum particle in an arbitrary one-dimensional potential has been developed. It has been proved that the wave function of an infinite motion can be expressed accurate to up two arbitrary constants with the use of one particular solution to the system of first-order linear differential equations. It has been shown that many well-known methods, such as the integral equation method, the transfer matrix method, the embedding method, and the method of combination of scattering parameters, are based on a general property of the solutions to the Schrödinger equation. Within the proposed approach, the relation between these methods becomes more transparent and their description can be well within a unified context.

Physics of the Solid StateJul 1, 20100 citations

Approximate solution of the Schrödinger equation for an atom in the field of a standing wave

Lilit A. Hovhannisyan, G. A. Muradyan, A. Zh. Muradyan

We present an approximate method of calculation of energy spectrum and wave functions of translational motion of a two-level atom in the field of a standing wave at zero value of the quasimomentum. Wave functions in the momentum representation are expressed in terms of confluent hypergeometric functions in case of continuous spectrum and in terms of Hermitian polynomials in case of discrete spectrum. The energy spectrum exhibits infinite compaction at transition from discrete part to continuous, as it is the case for, e.g., Coulombian potential.

Journal of Contemporary Physics (Armenian Academy of Sciences)Dec 26, 20130 citations

The Derivation of the Medium Wave Function in a One-Dimensional Finite Deep Symmetrical Square Potential Well

Zhao Peng-y

Three methods-a documental analysis, a textual method, a comprehensive analysis- are used in this article to analyze the energy levels of motional particles and their wave functions of one-dimensional finite deep symmetrical square potential wells, thus solving the eigen-values and eigen-functions at their corresponding energetic levels. Due to the three following advantages of a one-dimensional problem-its simpler mathematical processing, and the possible detailed-discussed results, and the display of the many features of quantum systems, so in the paper, the eigen-values and the exact formulas of the wave functions of moving particles in a one-dimensional finite deep symmetric square potential wells, which are not specified in the textbooks, are deviated according to the Schrodinger equation of stationary state through a case study of moving particles in a one-dimensional finite deep symmetric square potential wells.

集宁师范学院学报Jan 1, 20150 citations

Criteria for bound-state solutions in quantum mechanics

Carl A. Kocher

When does the Schrödinger equation have bound-state solutions? This question is pursued by a variational method with simple trial wave functions. An arbitrary one- or two-dimensional attractive potential is shown to have at least one discrete energy level, and estimates of the binding energy are obtained for shallow potential wells. In other problems, sufficient conditions are established for the existence of bound states.

American Journal of PhysicsJan 1, 197722 citations

Energy Spectrum of a Particle in an Infinitely Deep Potential Well with a Non-flat Bottom

S. I. Denisov, Stanislav Ivanovych Denysov, A.V. Husachenko +1 more

To model the quantum behavior of current carriers in heterogeneous nanostructures, different potential wells and barriers are widely used. Of particular interest are those (including artificial ones) for which the corresponding Schrödinger equation can be solved exactly. One of them is an infinitely deep potential well with a flat bottom defined as 𝑈(𝑥) = ∞ for |𝑥| ≥ 𝑎 and 𝑈(𝑥) = 0 for |𝑥| < 𝑎. Here, we report on exact solution of the stationary Schrödinger equation in the case, when the potential bottom is non-flat, i.e., 𝑈(𝑥) = −𝑓𝑥 (𝑓 > 0) if |𝑥| < 𝑎. Physically, this means that the particle in the well is subjected to an external force 𝑓 in the 𝑥-direction.

Jan 1, 20180 citations