Europhys. Lett.
Volume 62, Number 5, June 2003
Page(s) 622 - 628
Section General
Published online 01 May 2003
DOI: 10.1209/epl/i2003-00419-1
Europhys. Lett., 62 (5) , pp. 622-628 (2003)

Unitary transformation for the system of a particle in a linear potential

D.-Y. Song

Department of Physics, University of Florida - Gainesville, FL 32611, USA and Department of Physics, Sunchon National University - Suncheon 540-742, Korea

(Received 2 September 2002; accepted in final form 11 April 2003)

A unitary operator, which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely related to the one which is responsible for the existence of coherent states for a harmonic oscillator, is used to find a general wave packet described by an Airy function. The kernel (propagator) and a complete set of Hermite-Gaussian-type wave functions are also given.

03.65.Fd - Algebraic methods.
03.65.Ge - Solutions of wave equations: bound states.
42.25.Bs - Wave propagation, transmission and absorption.

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