On the Quantizations of the Damped Systems

TL;DR

This paper introduces a Hamiltonian framework for quantizing damped systems by decomposing second order differential equations into first order equations, exemplified on a damped harmonic oscillator, ensuring clear Schrödinger evolution.

Contribution

It presents a novel Hamiltonian approach to quantize damped systems, providing a consistent method for their quantum description.

Findings

Quantization of a damped harmonic oscillator achieved.

Unambiguous Schrödinger evolution demonstrated.

Framework applicable to other damped systems.

Abstract

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.