SUSY quantum mechanics with complex superpotentials and real energy spectra - INSPIRE

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SUSY quantum mechanics with complex superpotentials and real energy spectra

Alexander A. Andrianov
(
- St. Petersburg State U.
)
,
F. Cannata
(
- Bologna U. and
- INFN, Bologna
)
,
J.-P. Dedonder
(
- Paris U., VI-VII and
- Orsay, IPN
)
,
Mikhail V. Ioffe
(
- St. Petersburg State U.
)

Jun, 1998

22 pages

Published in:

Int.J.Mod.Phys.A 14 (1999) 2675-2688

e-Print:

quant-ph/9806019 [quant-ph]

DOI:

10.1142/S0217751X99001342

Report number:

SPBU-IP-97-24,
SPbU-IP-97-24

View in:

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Abstract:

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. We 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.

Note:

22 pages, Latex

References(25)

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