TY - JOUR

T1 - Exactly solvable two-dimensional complex model with a real spectrum

AU - Ioffe, M. V.

AU - Cannata, F.

AU - Nishnianidze, D. N.

N1 - Funding Information: This work was supported in part by the INFN, the University of Bologna (M. V. I. and D. N. N.), the Spanish Ministry of Education and Science (Grant No. SAB2004-0143, M. V. I.), and the Russian Federal Education Agency (Project No. RNP 2.1.1.1112, M. V. I.).

PY - 2006/7

Y1 - 2006/7

N2 - 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.

AB - 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.

KW - Complex potentials

KW - Intertwining relations

KW - Supersymmetric quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=33746322401&partnerID=8YFLogxK

U2 - 10.1007/s11232-006-0092-7

DO - 10.1007/s11232-006-0092-7

M3 - Article

AN - SCOPUS:33746322401

VL - 148

SP - 960

EP - 967

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -