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arXiv · 2105.03240

On the supersymmetry of the Klein-Gordon oscillator

Georg Junker
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Abstract

The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the spectral properties of the Klein-Gordon oscillator, which is closely related to that of the non-relativistic harmonic oscillator in three dimensions. Supersymmetry also enables us to derive a closed-form expression for the energy-dependent Green's function.

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Georg Junker. 2021-05-07. On the supersymmetry of the Klein-Gordon oscillator. https://doi.org/10.3390/sym13050835

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