Figure 1

Comparison between the time evolutions of a circular (solid line) and a spherical shell (dashed line) using the average radial position (top) and the average radial momentum (bottom) obtained from Eqs. (3, 9) for $a^{(2)}=15/7$ and $a^{(3)}=2$. On average the two-dimensional shell first contracts and then expands, whereas the three-dimensional one expands from the onset. In the left insets we show the short time behavior of a displaced Gaussian radial wave packet obtained numerically. Here we have used the same Gaussian for an initial radial wave function in two and three dimensions with $\delta r=0.4$ and $\rho =1.5$ in arbitrary units. Position is scaled in units of the initial position $r_0^{(N)}$ of the wave packet and momentum in terms of the final momentum $p_{\infty }^{(N)}$.Reuse & Permissions