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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Supersymmetric oscillator and the phase problem

K. S. Raghunathan, Thalanayar S. Santhanam

Published Jun 15, 1986• 2 citations
Publisher

Abstract

The doubling of the Hilbert space in supersymmetric quantum mechanics is shown to settle the problem of the phase of the harmonic oscillator.Received 5 March 1986DOI:https://doi.org/10.1103/PhysRevD.33.3790©1986 American Physical Society

DOI
10.1103/physrevd.33.3790

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The doubling of the Hilbert space in supersymmetric quantum mechanics is shown to settle the problem of the phase of the harmonic oscillator.Received 5 March 1986DOI:https://doi.org/10.1103/PhysRevD.33.3790©1986 American Physical Society
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.