On the Quantizations of the Damped Systems

Mod. Phys. Lett. A8 (1993) 2037-2044 Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the system of a linear damped harmonic oscillator and demonstrate that the time evolution of the Schr\"odinger equation is unambiguously determined.