Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

Author: Haas F.  

Publisher: Springer Publishing Company

ISSN: 0020-7748

Source: International Journal of Theoretical Physics, Vol.44, Iss.5, 2005-05, pp. : 609-617

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Abstract

The stochastic quantization method recently developed by Haba and Kleinert is extended to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation. Using a rescaling transformation, the Schrödinger equation for the time-dependent harmonic oscillator is obtained after averaging of a classical stochastic differential equation.