|
This article is cited in 16 scientific papers (total in 16 papers)
Exactly solvable two-dimensional complex model with a real spectrum
M. V. Ioffea, F. Cannatab, D. N. Nishnianidzeac a Saint-Petersburg State University
b University of Bologna, Department of Physics and INFN
c N. Muskhelishvili Kutaisi State Technical University
Abstract:
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.
Received: 24.10.2005
Citation:
M. V. Ioffe, F. Cannata, D. N. Nishnianidze, “Exactly solvable two-dimensional complex model with a real spectrum”, TMF, 148:1 (2006), 102–111; Theoret. and Math. Phys., 148:1 (2006), 960–967
Linking options:
https://www.mathnet.ru/eng/tmf2061https://doi.org/10.4213/tmf2061 https://www.mathnet.ru/eng/tmf/v148/i1/p102
|
Statistics & downloads: |
Abstract page: | 563 | Full-text PDF : | 232 | References: | 77 | First page: | 1 |
|