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Springer proceedings in physics

The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbert Space

Natália Bebiano, João da Providência

Published Jan 1, 2016• 6 citations
Publisher
DOI
10.1007/978-3-319-31356-6_10

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This paper is devoted to the construction of what we will call 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 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.