PT-Symmetric, Quasi-Exactly Solvable matrix Hamiltonians

Abstract

Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix quasi exactly solvable operators are constructed with the emphasis set on PT-symmetric Hamiltonians.

14 pages, 1 figure, one equation corrected, results added

References in corpus (11)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• A PT-Invariant Potential With Complex QES Eigenvalues
• Quasi-Exactly Solvable Systems and Orthogonal Polynomials
• Quasi Exactly Solvable 2$\times$2 Matrix Equations
• Quasi-Exact Solvability and the direct approach to invariant subspaces
• On quasi-exactly solvable matrix models
• Quasi Exactly Solvable NxN-Matrix Schroedinger Operators
• QES systems, invariant spaces and polynomials recursions
• Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold
• Quasi-exact minus-quartic oscillators in strong-core regime
• PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

Cited by in corpus (2)

• Quadratic Lie algebras and quasi-exact solvability of the two-photon Rabi Hamiltonian
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model