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Chinese Physics Letters

SUSY QM in a One-Dimensional Box and Local Observable Quantities

Salvatore, Vincenzo

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

我们在 one-dimensionalbox 为一个免费粒子调查几 Hamiltonians，在超级对称的量力学的上下文。明确地，我们与 Neumann 边界条件学习这个问题，周期并且抗周期性病药边界状况和复杂边界条件。这被使用为他们之一的地面状态特徵函数以概率密度和水流表示搭挡 Hamiltonians 的因式分解的最近建议的一条途径完成。

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•Apr 26, 2024•0 citations
我们在 one-dimensionalbox 为一个免费粒子调查几 Hamiltonians，在超级对称的量力学的上下文。明确地，我们与 Neumann 边界条件学习这个问题，周期并且抗周期性病药边界状况和复杂边界条件。这被使用为他们之一的地面状态特徵函数以概率密度和水流表示搭挡 Hamiltonians 的因式分解的最近建议的一条途径完成。
We investigate several Hamiltonians for a free particle in a one-dimensional box, in the context of supersymmetric quantum mechanics. Specifically, we study this problem with the Neumann boundary condition, the periodic and antiperiodic boundary condition, and some mixed and complex boundary conditions. This is achieved by using an approach recently proposed which expresses the factorization of the partner Hamiltonians in terms of the probability density and current for the ground-state eigenfunction of one of them.
This undergraduate thesis contains one dimensional introductory treatment of Supersymmetric Quantum Mechanics (SUSY QM). The factorisation method is used to obtain Partner Hamiltonians, and the notions of partner potentials and superpotential are introduced. It demonstrated how energy spectra and eigenfunctions of partner potentials can be correlated for the cases of unbroken and broken supersymmetry. Generalisations of these cases attributed to Sets of Hamiltonians and shape invariant potentials are introduced. The devel oped formalisation is used to obtain energy eigenfunctions and spectra of partner potentials of some well-known quantum systems, namely the Infinite Square Well and the Free Particle. In these systems, the partner potentials are trigonometric and hyperbolic functions, respectively. A comparison of these two physically distinct but mathematically related partner potentials is provided. A new philosophical interpretation of SUSY QM is introduced, with an ontological discussion of supersymmetric notions and SUSY QM. The current observation problem of SUSY is discussed, and on that basis, two opposing arguments are presented. The method of Falsification by Karl Popper is briefly introduced, and an argument is produced regarding its application to SUSY.