Supersymmetry in quantum mechanics: An extended view

Abstract

The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric, with space-time symmetries used for the explicit construction. No fermionic or Grassmann variables need to be invoked. Our construction extends supersymmetry to continuous spectra. Most notably, while the free particle in one dimension has generally been regarded as having a doubly degenerate continuum throughout, the construction clarifies taht there is a single zero energy state at the base of the spectrum.

4 pages, 4 figures

References in corpus (1)

• Supersymmetric Quantum Mechanics of Scattering

Cited by in corpus (6)

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• Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit
• Landau levels of a Dirac electron in graphene from non-uniform magnetic fields