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Fundamental World of Quantum Chemistry, A Tribute to the Memory of Per-Olov Lowdin, Volume 3, E. Brandas and E.S. Kryachko (Ed.) (2004) 67-96
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On supersymmetric quantum mechanics
Maurice R. Kibler1, Mohammed Daoud1

This paper constitutes a review on N=2 fractional supersymmetric 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.
1:  IPNL - Institut de Physique Nucléaire de Lyon
supersymmetry – fractional supersymmetric quantum mechanics – generalized Weyl-Heisenberg algebra – dynamical systems – fractional supersymmetric oscillator – deformed-bosons – k-fermions