SUSY QUANTUM MECHANICS WITH COMPLEX SUPERPOTENTIALS AND REAL ENERGY SPECTRA

A. A. ANDRIANOV, M. V. IOFFE, F. CANNATA, J.-P. DEDONDER
1999 International Journal of Modern Physics A  
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study in general the isospectrality between complex potentials. In very specific cases we can construct in a natural way "quasi-complex" potentials which we define as complex potentials having a global property such as to lead to a Hamiltonian with real spectrum.
more » ... e also obtained a class of complex transparent potentials whose Hamiltonian can be intertwined to a free Hamiltonian. We provide a variety of examples both for the radial problem (half axis) and for the standard one-dimensional problem (the whole axis), including remarks concerning scattering problems.
doi:10.1142/s0217751x99001342 fatcat:growtodtcvgnrl7hwmfkje3psa