Abstract
Presents a multidimensional Ermakov theory applicable to both separable and nonseparable time independent quantum mechanical systems, the separability of the system being determined by the separability of the wavefunction in configuration space. A consequence of the theory is the existence of a new exact invariant for multidimensional quantum systems. In one dimension the author shows that this new invariant reduces to the well known Ermakov-Lewis invariant. Two applications of the theory are given. In the first case a new exact invariant is obtained for planar optical and particle channelling systems. In the second case he obtains the Ermakov invariants and electron ray path equations for the hydrogen atom.
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