Multiplication of distributions in a linear gain and loss system

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 $H^{†}$. In the analysis carried out here, the role of {\em weak pseudo-bosonic} ladder operators is relevant.

in press in ZAMP

References in corpus (2)

• Bypassing the bandwidth theorem with PT symmetry
• Lagrangian for RLC circuits using analogy with the classical mechanics concepts

Cited by in corpus (1)

• Extended coupled SUSY, pseudo-bosons and weak squeezed states