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AIP conference proceedings

Charged Particle in a Time-dependent Electric Field: A White Noise Functional Approach

E. B. Gravador, Jinky B. Bornales, M. J. Liwanag, Christopher Casenas Bernido, M. Victoria Carpio-Bernido

Published Jan 1, 2008• 0 citations
Publisher

Abstract

The propagator for a charged particle in a time‐dependent electric field is calculated following Hida and Streit's framework [1] where the propagator is the T‐transform of Feynman functional. However, we have to regard the potential V = −qE(τ)x≡mℏξ̇x following C. C. Bernido and M. V. Carpio‐Bernido's [2] prescription of time‐dependent potentials. The result agrees with the limiting form of Eqn. (16) of N. Morgenstern Horing, H. L. Cui, and G. Fiorenza [3], when the magnetic field is switched off, and Eqn. (17) of [3] when the electric field is constant in time.

DOI
10.1063/1.2956802

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The propagator for a charged particle in a time‐dependent electric field is calculated following Hida and Streit's framework [1] where the propagator is the T‐transform of Feynman functional. However, we have to regard the potential V = −qE(τ)x≡mℏξ̇x following C. C. Bernido and M. V. Carpio‐Bernido's [2] prescription of time‐dependent potentials. The result agrees with the limiting form of Eqn. (16) of N. Morgenstern Horing, H. L. Cui, and G. Fiorenza [3], when the magnetic field is switched off, and Eqn. (17) of [3] when the electric field is constant in time.
Through a sequence of time-dependent transformations and time substitution, we evaluate the propagator of a harmonically bound charged particle with time-dependent mass in a time-varying electromagnetic field by relating it to those of free particles. From this propagator we derive the wave functions. The propagators beyond and at caustics are then investigated, respectively, by including the Maslov phase factor and by using the modified semigroup property. Finally, we calculate explicitly the propagator for the constant-damping case.