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arXiv:quant-ph/0702181

Stationary states in a potential well

Haret Codratian Rosu, José Luis Morán-López

Published Feb 18, 2007• 1 citation
arXivHTMLPDF

Abstract

We review here in a historical context the topic of stationary states in the quantum world, including the generalization to the primary ideas. We also discuss the stationary states in one dimensional parabolic wells and the three dimensional Coulomb and parabolic cases, as well as the stationary bound states in the continuum
DOI
10.48550/arxiv.quant-ph/0702181

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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.
The deterministic many-interacting-worlds method proposed in 2014 showed potential among the numerous interpretation of quantum mechanics. The successful application of this method in harmonic oscillator has been promoted for a long time. In this article we continue the idea about using this method to solve some bounded systems different from harmonic oscillator potential and extend to 2 dimension cases. We focus on the potential with singularity like coulomb potential and finite trap potential by some asymptotic smooth method. The numerical simulation mainly based on the dynamical algorithm proposed in many-interacting-worlds method will be used to approach the stationary states of given systems. Our results shows the consistency to the matrix Numerov method in standard quantum mechanics in solving bounded systems and provides the possibility to solve more complex systems.