Quantum Description of a Damped Coupled Harmonic Oscillator via White-Noise Analysis

Abstract

In this paper, the quantum mechanical dynamics of a particle subjected to a damped coupled harmonic oscillator potential was investigated by solving its quantum propagator using the Hida-Streit formulation—also known as the White-Noise analysis. A coordinate transformation to decouple the system was also performed. After the decoupling process, the authors obtained a separate expression of the Lagrangian for a one-dimensional damped harmonic oscillator. Then, the obtained Lagrangian was cast to the classical action and evaluated their propagator using the white noise path integration. The full form of the propagator was solved by taking the product of the individual propagator, and from that, the wave function, particularly the ground state wave function was extracted by symmetrization and setting the quantum number n1 = n2 = 0. The result agrees with the propagator of a coupled harmonic oscillator without damping (Pabalay et.al, 2007) as the damping factor ? is turned off.