文章基本信息

标题：Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics
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作者：Timothy Brian Huber
期刊名称：The Indiana University Journal of Undergraduate Research
印刷版ISSN：2379-5611
出版年度：2018
卷号：4
期号：1
页码：1-9
出版社：Indiana University Bloomington
摘要：The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.
关键词：exact solutions; time;dependent Schrödinger equation; time;independent Schrödinger equation; supersymmetric quantum mechanics; intertwining operators