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

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