A new non-Hermitian E2-quasi-exactly solvable model

Abstract

We construct a previously unknown $E_2$-quasi-exactly solvable non-Hermitian model whose eigenfunctions involve weakly orthogonal polynomials obeying three-term recurrence relations that factorize beyond the quantization level. The model becomes Hermitian when one of its two parameters is fixed to a specific value. We analyze the double scaling limit of this model leading to the complex Mathieu equation. The norms, Stieltjes measures and moment functionals are evaluated for some concrete values of one of the two parameters.

8 pages

References in corpus (16)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermitian Representation of Quantum Mechanics
• A PT-Invariant Potential With Complex QES Eigenvalues
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• Quasi-Exactly Solvable Systems and Orthogonal Polynomials
• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
• Invisible defects in complex crystals
• Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials
• A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
• New Quasi-Exactly Solvable Sextic Polynomial Potentials
• Use of Equivalent Hermitian Hamiltonian for $PT$-Symmetric Sinusoidal Optical Lattices
• E2-quasi-exact solvability for non-Hermitian models
• Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type
• Non-Hermitian systems of Euclidean Lie algebraic type with real eigenvalue spectra
• A complex periodic QES potential and exceptional points

Cited by in corpus (5)

• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• E2-quasi-exact solvability for non-Hermitian models
• Displaced harmonic oscillator $V\sim \min [(x+d{)}^2,(x-d{)}^2]$ as a benchmark double-well quantum model
• Stability boundaries of a Mathieu equation having PT symmetry
• A unifying E2-quasi-exactly solvable model