Improved constraints on states bound by a class of potentials

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Abstract
Recent work on states bound by a central potential whose Laplacian is positive is extended to cover a wider class of potentials for which energy level ordering theorems can be proved. This class includes power law potentials in particular. Constraints on the moments of the radial distance are improved and similarly for the kinetic energy. These constraints are shown to provide tight bounds on the energies of ground states for power law potentials, and on their variation with angular momentum. They are also used to bound the position of the maximum of the wavefunction for these states.

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