Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy

Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrödinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium. We find, for specific choices of initial parameters, that as much as 90% of the kinetic energy can be localized (at least conceptually) in the 'front half' of such Gaussian wave packets, and we visualize these effects.