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An extended phase-space SUSY quantum mechanics. (English) Zbl 1155.81022
Summary: In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0+1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N=2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.
81Q60Supersymmetry and quantum mechanics
81S30Phase space methods in quantum mechanics