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arXiv · 1609.07579

Intertwining operators for non self-adjoint Hamiltonians and bicoherent states

Fabio Bagarello
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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.

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Fabio Bagarello. 2016-09-24. Intertwining operators for non self-adjoint Hamiltonians and bicoherent states. https://doi.org/10.1063/1.4964128

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