Representations of commutation relations in Dissipative Quantum Mechanics

TL;DR

This paper establishes the uniqueness of solutions to certain quantum commutation relations and provides rigorous mathematical foundations for phenomena like exponential decay in resonant quantum states.

Contribution

It proves a uniqueness theorem for restricted Weyl commutation relations and addresses mathematical issues related to continuous quantum system monitoring and decay phenomena.

Findings

Proved the uniqueness of solutions to restricted Weyl commutation relations.

Provided rigorous foundations for exponential decay in resonant quantum states.

Discussed mathematical problems related to continuous monitoring of quantum systems.

Abstract

We prove the uniqueness theorem for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions that are close to unitaries. We also discuss related mathematical problems of continuous monitoring of quantum systems and provide rigorous foundations for the exponential decay phenomenon of a resonant state in quantum mechanics.