Volume 62, Number 5, June 2003
|Page(s)||622 - 628|
|Published online||01 May 2003|
Unitary transformation for the system of a particle in a linear potential
Department of Physics, University of Florida - Gainesville, FL 32611, USA and Department of Physics, Sunchon National University - Suncheon 540-742, Korea
Accepted: 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.
PACS: 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
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