Title

Quantizing the damped harmonic oscillator

Document Type

Article

Publication Date

2005

Publication Title

Journal of Physics A: Mathematical and General

Department

Physics

Abstract

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that the unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.

ISSN

0305-4470