Multiplication of distributions in a linear gain and loss system

• URL: http://arxiv.org/abs/2306.02386v1
• Date: Sun, 4 Jun 2023 15:42:55 GMT
• Title: Multiplication of distributions in a linear gain and loss system
• Authors: Fabio Bagarello
• Abstract summary: We propose a new definition of multiplication between distributions. In the analysis carried out here, the role of em weak pseudo-bosonic ladder operators is relevant.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $H^\dagger$. In the analysis carried out here, the role of {\em weak pseudo-bosonic} ladder operators is relevant.

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