Intertwining operators for non self-adjoint Hamiltonians and bicoherent states

Abstract

This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some {\em minimal ingredients}. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.

In press in Journal of Mathematical Physics

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• Non Hermitian Operators with Real Spectrum in Quantum Mechanics

Cited by in corpus (1)

• Coordinate representation for non Hermitian position and momentum operators