Unitary transformation for the system of a particle in a linear potential
Abstract
A unitary operator, which relates the system of a particle in a linear potential with timedependent 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 HermiteGaussian type wave functions are also given.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 June 2003
 DOI:
 10.1209/epl/i2003004191
 arXiv:
 arXiv:quantph/0211107
 Bibcode:
 2003EL.....62..622S
 Keywords:

 03.65.Fd;
 03.65.Ge;
 42.25.Bs;
 Algebraic methods;
 Solutions of wave equations: bound states;
 Wave propagation transmission and absorption;
 Quantum Physics
 EPrint:
 Europhysics Letters (in press)