Re-establishing supersymmetry between harmonic oscillators in $D \neq 1$ dimensions

Using a PT symmetric regularization technique we reminad the reader that and how (a) the SUSY is re-established between the two shifted harmonic oscillator potentials $V(q)=q^2+{G}/{q^2}+ const$ and (b) many non-equivalent Hermitian and non-Hermitian (PT symmetric) systems may often be studied in parallel (with a schematic solvable illustrative example added).

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