On the supersymmetry of the Klein-Gordon oscillator

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.

Dedicated to Akira Inomata on the occasion of his 90${}^{\mathbf{th}}$ birthday. 7 pages

References in corpus (5)

• Relativistic quantum oscillators in the global monopole spacetime
• The generalized Klein-Gordon oscillator in the background of cosmic string space-time with a linear potential in the Kaluza-Klein theory
• Supersymmetric Dirac-Hamiltonians in $(1+1)$ dimensions revisited
• The study of the generalized Klein-Gordon oscillator in the context of the Som-Raychaudhuri space-time
• Power law duality in classical and quantum mechanics

Cited by in corpus (3)

• From orthosymplectic structure to super topological matter
• Klein-Gordon equation within the real Hilbert space formalism
• Supersymmetric Klein-Gordon and Dirac oscillators