We derive from a dynamical symmetry property that the linear and nonlinear Schrödinger equations with harmonic potential possess an infinite string of shape-preserving coherent wave-packet states with classical motion. Unlike the Schrödinger state with $\Delta x\Delta p=\frac{\hslash }{2}$, the uncertainty product can be arbitrarily large for these states showing that classical motion is not necessarily linked with minimum uncertainty. We obtain a generalization of Sudarshan's diagonal coherent-state representation in terms of these states.

• Received 30 March 1981

DOI:https://doi.org/10.1103/PhysRevD.25.3413