Intertwining operators for non self-adjoint Hamiltonians and bicoherent states

TL;DR

This paper develops exactly solvable quantum models using intertwining operators for non self-adjoint Hamiltonians, introduces bicoherent states, and explores their properties and applications in quantization across finite and infinite-dimensional spaces.

Contribution

It constructs explicit non self-adjoint Hamiltonian models and introduces bicoherent states for quantization, expanding the toolkit for PT-quantum mechanics.

Findings

Explicit construction of non self-adjoint Hamiltonians with known spectra

Introduction and analysis of bicoherent states

Applications demonstrated in finite and infinite-dimensional systems

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.