Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

TL;DR

This paper explores how multiple supercharges in one-dimensional quantum mechanics reveal hidden symmetries in super-Hamiltonians, especially for periodic and finite bound state potentials, through algebraic and analytic analysis.

Contribution

It provides a rigorous analysis of hidden-symmetry operators arising from supersymmetry in one-dimensional quantum systems, with new theorems and illustrative examples.

Findings

Hidden symmetries are linked to supercharges forming a superalgebra.

The paper characterizes algebraic and analytic properties of hidden-symmetry operators.

Examples demonstrate the application of theoretical results.

Abstract

When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.