caa a22 4500 467910669 CHVBK 20180406152848.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s11232-006-0092-7 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0092-7 Exactly solvable two-dimensional complex model with a real spectrum [Elektronische Daten] [M. Ioffe, F. Cannata, D. Nishnianidze] 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. Springer Science+Business Media, Inc., 2006 supersymmetric quantum mechanics nationallicence intertwining relations nationallicence complex potentials nationallicence Ioffe M. St. Petersburg State University, St. Petersburg, Russia aut Cannata F. Dipartimento di Fisica and INFN, Bologna, Italy aut Nishnianidze D. St. Petersburg State University, St. Petersburg, Russia aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 148/1(2006-07-01), 960-967 0040-5779 148:1<960 2006 148 11232 https://doi.org/10.1007/s11232-006-0092-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0092-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ioffe M. St. Petersburg State University, St. Petersburg, Russia aut NATIONALLICENCE 700 1- Cannata F. Dipartimento di Fisica and INFN, Bologna, Italy aut NATIONALLICENCE 700 1- Nishnianidze D. St. Petersburg State University, St. Petersburg, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 148/1(2006-07-01), 960-967 0040-5779 148:1<960 2006 148 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer