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.

Bagarello, F. (2016). Intertwining operators for non-self-adjoint hamiltonians and bicoherent states. JOURNAL OF MATHEMATICAL PHYSICS, 57(10), 103501-1-103501-19 [10.1063/1.4964128].

Intertwining operators for non-self-adjoint hamiltonians and bicoherent states

BAGARELLO, Fabio
2016-01-01

Abstract

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.
2016
Settore MAT/07 - Fisica Matematica
Bagarello, F. (2016). Intertwining operators for non-self-adjoint hamiltonians and bicoherent states. JOURNAL OF MATHEMATICAL PHYSICS, 57(10), 103501-1-103501-19 [10.1063/1.4964128].
File in questo prodotto:
File Dimensione Formato  
2016JMP2.pdf

Solo gestori archvio

Dimensione 675.1 kB
Formato Adobe PDF
675.1 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/222445
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 12
social impact