Prepotential approach to systems with dynamical symmetries

TL;DR

This paper introduces a prepotential method for constructing quantum systems with dynamical symmetries, generalizing classical models like hydrogen and harmonic oscillator to include position-dependent mass, and solving them algebraically.

Contribution

The paper proposes a novel prepotential approach to build and solve quantum systems with dynamical symmetries, extending classical models to new regimes.

Findings

Derived generalized hydrogen and harmonic oscillator models with position-dependent mass

Systems retain similar symmetries and are solvable algebraically

Method provides a new framework for constructing symmetric quantum systems

Abstract

A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have the symmetries which are similar to the corresponding ones, and can be solved by using the algebraic method.