The Interplay of supersymmetry and PT symmetry in quantum mechanics: A Case study for the Scarf II potential
200211 pages
Published in:
- J.Phys.A 35 (2002) 8793
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Abstract: (IOP)
Motivated by the duality of normalizable states and the presence of the quasi-parity quantum numberq= ± 1 insymmetric (non-Hermitian) quantum mechanical potential models, the relation ofsymmetry and supersymmetry (SUSY) is studied. As an illustrative example, theinvariant version of the Scarf II potential is presented, and it is shown that the 'bosonic' Hamiltonian has twodifferent'fermionic' SUSY partner Hamiltonians (potentials) generated from the ground-state solutions withq= 1 andq= −1. It is shown that the 'fermionic' potentials cease to beinvariant when thesymmetry of the 'bosonic' potential is spontaneously broken. A modifiedsymmetry inspired SUSY construction is also discussed, in which the SUSY charge operators contain the antilinear operator. It is shown that in this scheme the 'fermionic' Hamiltonians are just the complex conjugates of the original 'fermionic' Hamiltonians, and thus possess the same energy eigenvalues.References(50)
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