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Discrete Symmetries and Supersymmetries - Powerful Tools for Studying Quantum Mechanical Systems

Jiri Niederle

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

Dicrete symmetries( DS) of the Schrodinger-Pauli equation are applied to reduction of this equation and search for its hidden supersymmetries. General problems of using of DS in quantum mechanics are discussed. 1

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Eclética Química•Dec 8, 1997•0 citations
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we introduce the supersymmetric oscilator and, next, we generalize these concepts to introduce the fundamentals of Supersymmetric Quantum Mechanics. We also discuss useful tools to solve problems in Quantum Mechanics which are intrinsecally related to Supersymmetry as hierarchy of hamiltonians and shape invariance. We present two approximation methods which will be specially useful: the well known Variational Method and the Logarithmic Perturbation Theory, the latter being closely related to the concepts of superpotentials and hierarchy of hamiltonians. Finally, we present problems related to superpotentials which are monomials in even powers of the x coordinate multiplied by the sign function epsilon(x), which seems to be a new class of problems in Supersymmetric Quantum Mechanics.