We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system, we propose a new definition of multiplication between distributions, and we check that this definition can be adopted when checking the biorthonormality of the eigenstates of the Hamiltonian H of the system, and of its adjoint H-& DAG;. In the analysis carried out here, the role of weak pseudo-bosonic ladder operators is relevant.

Bagarello, F. (2023). Multiplication of distributions in a linear gain and loss system. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 74(4) [10.1007/s00033-023-02038-1].

Multiplication of distributions in a linear gain and loss system

Bagarello, F.
2023-08-01

Abstract

We consider a model of coupled oscillators which can be seen as a gain and loss system. In the attempt to quantize the system, we propose a new definition of multiplication between distributions, and we check that this definition can be adopted when checking the biorthonormality of the eigenstates of the Hamiltonian H of the system, and of its adjoint H-& DAG;. In the analysis carried out here, the role of weak pseudo-bosonic ladder operators is relevant.
ago-2023
Settore MAT/07 - Fisica Matematica
Bagarello, F. (2023). Multiplication of distributions in a linear gain and loss system. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 74(4) [10.1007/s00033-023-02038-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/637215
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