Quantum Integrals of Motion for Variable Quadratic Hamiltonians
Ricardo Cordero-Soto, Erwin Suazo, Sergei K. Suslov
TL;DR
This paper develops a method to construct quantum integrals of motion for variable quadratic Hamiltonians, extending existing invariants, and analyzes the energy evolution in quantum damped oscillators.
Contribution
It introduces an extended form of Lewis-Riesenfeld invariants for quantum damped oscillators with variable quadratic Hamiltonians.
Findings
Constructed integrals of motion for quantum damped oscillators.
Extended Lewis-Riesenfeld dynamical invariants.
Analyzed energy expectation value evolution.
Abstract
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
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