Dynamics of zero-energy nonspreading non-Gaussian wave packets for a class of central potentials

Zero-energy wave packets, coherent states, are constructed in such a way that they retain their shape during the time evolution for a large class of central potentials. The packets are not of the Gaussian type with −r2 dependence but, instead, their shape is determined by −r1μ+1/2 with −1/2<μ<1/2. A very close quantum-classical correspondence is also shown, i.e., the well localized states travel along suitable classical trajectories.