Supersymmetry and a Time-Dependent Landau System
V. Alan Kosteleck\'y, V. I. Man'ko, Michael Martin Nieto, and D., Rodney Truax
TL;DR
This paper develops a method to analyze supersymmetry in a charged spin-1/2 particle within a time-dependent magnetic field, demonstrating a physical realization of supersymmetric quantum mechanics and constructing supercoherent states.
Contribution
It introduces a general technique for studying supersymmetry in time-varying electromagnetic fields and applies it to a Landau system with a uniform magnetic induction.
Findings
Supersymmetry can be realized in a time-dependent Landau system.
Group-theoretic methods effectively solve the Schrödinger equations.
Supercoherent states are explicitly constructed for the system.
Abstract
A general technique is outlined for investigating supersymmetry properties of a charged spin- quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schr\"odinger equations and obtain eigensolutions. The supercoherent states for this system are constructed.
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