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We provide simple examples of closed-form Gaussian wavepacket solutions ofthe free-particle Schrodinger equation in one dimension which exhibit the mostgeneral form of the time-dependent spread in position, namely (Delta x_t)^2 =(Delta x_0)^2 + At + (Delta p_0)^2t^2/m^2, where A = <(xhat - <xhat>_0)(phat -<phat>_0) + (phat - <phat>_0)(xhat - <xhat>_0)>_0 contains information on theposition-momentum correlation structure of the initial wave packet. We exhibitstraightforward examples corresponding to squeezed states, as well asquasi-classical cases, for which A < 0 so that the position spread can (atleast initially) decrease in time because of such correlations. We discuss howthe initial correlations in these examples can be dynamically generated (atleast conceptually) in various bound state systems. Finally, we focus onproviding different ways of visualizing the x-p correlations present in thesecases, including the time-dependent distribution of kinetic energy and the useof the Wigner quasi-probability distribution. We discuss similar results, bothfor the time-dependent Delta x_t and special correlated solutions, for the caseof a particle subject to a uniform force.Comment: 25 pages, 2 embedded postscript figure

foundations of physics letters

Simple Examples of Position-Momentum Correlated Gaussian Free-Particle Wave Packets in One Dimension With the General Form of the Time-Dependent Spread in Position