Exactly solvable two-dimensional complex model with a real spectrum
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 1, pp. 102-111
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Using supersymmetric intertwining relations of the second order in
derivatives, we construct a two-dimensional quantum model with a complex
potential for which all energy levels and the corresponding wave functions
are obtained analytically. This model does not admit separation of variables
and can be considered a complexified version of the generalized
two-dimensional Morse model with an additional $\sinh^{-2}$ term. We prove
that the energy spectrum of the model is purely real. To our knowledge, this
is a rather rare example of a nontrivial exactly solvable model in two
dimensions. We explicitly find the symmetry operator, describe the
biorthogonal basis, and demonstrate the pseudo-Hermiticity of the Hamiltonian
of the model. The obtained wave functions are simultaneously eigenfunctions
of the symmetry operator.
Keywords:
supersymmetric quantum mechanics, intertwining relations, complex potentials.
@article{TMF_2006_148_1_a8,
author = {M. V. Ioffe and F. Cannata and D. N. Nishnianidze},
title = {Exactly solvable two-dimensional complex model with a real spectrum},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {102--111},
publisher = {mathdoc},
volume = {148},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_1_a8/}
}
TY - JOUR AU - M. V. Ioffe AU - F. Cannata AU - D. N. Nishnianidze TI - Exactly solvable two-dimensional complex model with a real spectrum JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2006 SP - 102 EP - 111 VL - 148 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2006_148_1_a8/ LA - ru ID - TMF_2006_148_1_a8 ER -
%0 Journal Article %A M. V. Ioffe %A F. Cannata %A D. N. Nishnianidze %T Exactly solvable two-dimensional complex model with a real spectrum %J Teoretičeskaâ i matematičeskaâ fizika %D 2006 %P 102-111 %V 148 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2006_148_1_a8/ %G ru %F TMF_2006_148_1_a8
M. V. Ioffe; F. Cannata; D. N. Nishnianidze. Exactly solvable two-dimensional complex model with a real spectrum. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 1, pp. 102-111. http://geodesic.mathdoc.fr/item/TMF_2006_148_1_a8/