Unitary transformation for the system of a particle in a linear potential
arXiv:quant-ph/0211107 · doi:10.1209/epl/i2003-00419-1
Abstract
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.
Europhysics Letters (in press)