• DOI:10.1007/978-94-017-0448-9_5
• Corpus ID: 117205409

On Supersymmetric Quantum Mechanics

@article{Kibler2004OnSQ,
  title={On Supersymmetric Quantum Mechanics},
  author={Maurice R. Kibler and Mohammed Daoud},
  journal={arXiv: Quantum Physics},
  year={2004},
  pages={67-96}
}

• M. Kibler, M. Daoud
• Published 25 September 2004
• Physics
• arXiv: Quantum Physics

This paper constitutes a review on N = 2 fractional supersym-metric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W k . It is shown how a general Hamiltonian can be associated with the algebra W k . This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, Poschl-Teller system, fractional supersymmetric oscillator of order k, etc.). The case of ordinary supersymmetric Quantum Mechanics corresponds to k = 2. A connection between fractional supersymmetric Quantum Mechanics and ordinary supersymmetric Quantum Mechanics is briefly described. A realization of the algebra W k , of the N = 2 supercharges and of the corresponding Hamiltonian is given in terms of deformed-bosons and k-fermions as well as in terms of differential operators.