General Solution of the Quantum Damped Harmonic Oscillator II : Some Examples

TL;DR

This paper provides explicit, compact solutions for the quantum damped harmonic oscillator's master equation, including a novel solution for initial states based on coherent states, advancing understanding of quantum dissipative systems.

Contribution

It introduces explicit, compact solutions for the quantum damped harmonic oscillator's master equation, including the first known solution for initial coherent states.

Findings

Explicit solutions for specific initial states

Compact form for coherent state initial conditions

Extension of previous general solution

Abstract

In the preceding paper (arXiv : 0710.2724 [quant-ph]) we have constructed the general solution for the master equation of quantum damped harmonic oscillator, which is given by the complicated infinite series in the operator algebra level. In this paper we give the explicit and compact forms to solutions (density operators) for some initial values. In particular, the compact one for the initial value based on a coherent state is given, which has not been given as far as we know. Moreover, some related problems are presented.