Calculation of the propagator of Schrödinger's equation on $(0,\infty )$ with the potential $k{x}^{-2}+{\omega }^2{x}^2$ by Lie symmetry group method

Abstract

The propagators (fundamental solutions) of the heat and Schrödinger's equations on the half-line with a combined harmonic oscillator and inverse-square potential calculated in the recent paper [{\em J. Math. Phys.} {\bf 59}, 051507 (2018)] using Laplace's method are demonstrated to be obtainable alternatively within the framework of symmetry group methods discussed in a series of two papers in the same journal.

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