Extended Jaynes-Cummings models and (quasi)-exact solvability

The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of space-time reflection symmetry (PT symmetry). However the new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi exactly solvable with a real algebraic part of their spectrum.Comment: 16 pages, 3 figures, discussion extended, one section adde

PT-Symmetric, Quasi-Exactly Solvable matrix Hamiltonians

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.Comment: 14 pages, 1 figure, one equation corrected, results adde