A Potential Based Quantization Procedure of the Damped Oscillator

TL;DR

This paper develops a quantization method for the damped oscillator using a potential-based approach, leading to an exact damping wave solution and a framework for describing quantum dissipation.

Contribution

It introduces a novel quantization procedure for dissipative systems based on the Lagrangian framework, enabling the study of quantum losses in damping systems.

Findings

Derived the damping quantum wave equation for the dissipative oscillator.

Obtained an exact damping wave solution to the quantum wave equation.

Established a theoretical framework for irreversible quantum systems with dissipation.

Abstract

Nowadays, two of the most prospering fields of physics are quantum computing and spintronics. In both, the loss of information and dissipation plays a crucial role. In the present work we formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned, and creates a theoretical frame to overcome these issues in the future. Based on the Lagrangian framework of the damped spring system, the canonically conjugated pairs and the Hamiltonian of the system are obtained, by which the quantization procedure can be started and consistently applied. As a result, the damping quantum wave equation of the dissipative oscillator is deduced, by which an exact damping wave solution of this equation is obtained. Consequently, we arrive at such an irreversible quantum theory by which the quantum losses can be described.