The Schrödinger–Langevin equation: Special solutions and nonexistence of solitary waves

Abstract

Two types of solutions of the Schrödinger–Langevin equation are investigated. It is proved that a special type of Gaussian solutions exist globally in time for the harmonic oscillator Hamiltonian. Furthermore, it is shown that the Schrödinger–Langevin equation can have no solitary wave type solutions in the damped free-particle case which lie in L2.