Conditions for complex spectra in a class of PT symmetric potentials

Abstract

We study a wide class of solvable PT symmetric potentials in order to identify conditions under which these potentials have regular solutions with complex energy. Besides confirming previous findings for two potentials, most of our results are new. We demonstrate that the occurrence of conjugate energy pairs is a natural phenomenon for these potentials. We demonstrate that the present method can readily be extended to further potential classes.

13 pages

References in corpus (1)

• Comprehensive analysis of conditionally exactly solvable models

Cited by in corpus (36)

• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Spontaneous breakdown of PT symmetry in the solvable square-well model
• PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• PT symmetry of a conditionally exactly solvable potential
• Conditional observability
• Solvability and PT-symmetry in a double-well model with point interactions
• Quantum catastrophes: a case study
• An exactly solvable PT symmetric potential from the Natanzon class
• Isospectral partners for a complex PT-invariant potential
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Should PT symmetric quantum mechanics be interpreted as nonlinear?
• Pseudo Hermitian Generalized Dirac Oscillators
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians
• Remarks on PT-pseudo-norm in PT-symmetric quantum mechanics
• Coherent states of non-Hermitian quantum systems
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• PT-symmetric regularizations in supersymmetric quantum mechanics
• Analytical solutions for the radial Scarf II potential
• Non-Hermitian Hamiltonians and similarity transformations
• New Exactly Solvable Isospectral Partners for PT Symmetric Potentials
• Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Which Metrics Are Consistent with a Given Pseudo-Hermitian Matrix?
• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Classification of the conditionally observable spectra exhibiting central symmetry
• Invariant Eigen-Structure in Complex-Valued Quantum Mechanics
• Mathematical and physical meaning of the crossings of energy levels in $\mathcal{P}\mathcal{T}-$symmetric systems
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator
• On the simpleness of zeros of Stokes multipliers