Europhys. Lett., 62 (5) , pp. 622-628 (2003)
Unitary transformation for the system of a particle in a linear potentialD.-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.
© EDP Sciences 2003