Exactly Solvable Two-Dimensional Complex Model with Real Spectrum

Details Exactly Solvable Two-Dimensional Complex Model with Real Spectrum Exactly Solvable Two-Dimensional Complex Model with Real Spectrum

2005-12-09

arxiv.org/abs/hep-th/0512110v1

Theor.Math.Phys.148:960-967,2006; Teor.Mat.Fiz.148:102-111,2006

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

Supersymmetrical intertwining relations of second order in derivatives allow to construct a two-dimensional quantum model with complex potential, for which {\it all} energy levels and bound state wave functions are obtained analytically. This model {\it is not amenable} to separation of variables, and it can be considered as a specific complexified version of generalized two-dimensional Morse model with additional $\sinh^{-2}$ term. The energy spectrum of the model is proved to be purely real. To our knowledge, this is a rather rare example of a nontrivial exactly solvable model in two dimensions. The symmetry operator is found, the biorthogonal basis is described, and the pseudo-Hermiticity of the model is demonstrated. The obtained wave functions are found to be common eigenfunctions both of the Hamiltonian and of the symmetry operator.

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