Expansion of the Time-Dependent Wavefunction in Quasistationary Energy Eigenfunctions

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Abstract
The motion of a wave packet moving in a potential well with a penetrable barrier is considered. A formally exact expression for the evolution operator is given as a sum over quasistationary energy eigenfunctions plus a remainder term. Numerical calculations are carried out for the square barrier potential. The approximation in which one neglects the remainder term is shown to be a useful and accurate one in computing properties of the particle which depend on the value of the wavefunction inside the potential well.