Related papers: A note on a classical dynamical system and its quantization

A note on a classical dynamical system and its quantization

URL: http://arxiv.org/abs/2506.21989v1
Date: Fri, 27 Jun 2025 07:56:15 GMT
Title: A note on a classical dynamical system and its quantization
Authors: Fabio Bagarello,
Abstract summary: We show that the Hamiltonian of the system, when quantized, produces different behaviors, depending on some relations between its parameters.<n>The two cases are analyzed in terms of bosonic or pseudo-bosonic ladder operators.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be recovered for any choice of its parameters. In this paper we consider this system and we show that, at a quantum level, it is not necessarily dissipative. In particular we show that the Hamiltonian of the system, when quantized, produces different behaviors, depending on some relations between its parameters. In fact, it gives rise to either a two dimensional (standard) harmonic oscillator, or to two independent oscillators, one of which is again {\em standard}, and a second one which is an inverted oscillator. The two cases are analyzed in terms of bosonic or pseudo-bosonic ladder operators, and the appearance of distributions for the inverted oscillator is commented.

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