The concept of supersymmetry in a quantum-mechanical system is extended, permitting the recognition of more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric upon taking into account physical reasonableness of the wavefunctions involved. Spacetime symmetries are used for the construction of the supercharges without explicit invocation of fermionic or Grassmann variables. Most notably, while the free particle in one dimension has generally been regarded as having a doubly degenerate continuum throughout, the construction clarifies that there is a single zero-energy state at the base of the spectrum.
Publication Source (Journal or Book title)
Journal of Physics A: Mathematical and General
Rau, A. (2004). Supersymmetry in quantum mechanics: An extended view. Journal of Physics A: Mathematical and General, 37 (43), 10421-10427. https://doi.org/10.1088/0305-4470/37/43/028