Wave Function Evolution of a Dissipative System

TL;DR

This paper provides an exact, path-integral-free solution for the wave function of a dissipative quantum system coupled to a bath, clarifying its structure and deriving the Weisskopf-Wigner linewidth theory.

Contribution

It introduces a simple, exact wave function solution for dissipative systems with Ohmic friction, separating system and bath effects in independent Hilbert spaces.

Findings

Exact wave function solution for dissipative systems

Clear separation of system and bath effects

Derivation of Weisskopf-Wigner linewidth theory

Abstract

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.