Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution

Abstract

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must include also the corresponding associated functions. In the specific case of anharmonic second-plus-fourth order interaction, expressions for the wave functions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wave functions is given.

17 p.p

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model

Cited by in corpus (5)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Expectation value dynamics within real Hilbert space quantum mechanics
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Dynamical symmetry algebra of two superintegrable two-dimensional systems
• Deformed angular momentum algebra within the real Hilbert space