A Comment on the Propagator of the Radial Oscillator

TL;DR

This paper demonstrates how time-dependent transformations can simplify deriving the propagator for a radial oscillator, highlighting their usefulness even in time-independent quantum systems.

Contribution

It combines recursion relations for shape invariant potentials with variable transformations to explicitly derive the propagator for a radial oscillator.

Findings

Time-dependent transformations aid in deriving propagators.

The approach simplifies calculations for quantum oscillators.

Explicit derivation confirms the utility of hybrid methods.

Abstract

Using a hybrid approach, based on the recursion relations for shape invariant potentials developed by Das and Huang and a time-dependent tranformation of variables, we derive the propagator for a radial oscillator. Although this is not a new result, we explicitly show that time-dependent tranformations are very beneficial even within the context of time-independent Hamiltonians in quantum mechanics.