Abstract
Given an eigenstate of a time-independent Hamiltonian, an equation is derived which generates the corresponding energy by means of a pointwise application of only the kinetic operator. Satisfaction of the equation at all points in configuration space, for arbitrary values of a scale factor, constitutes a necessary eigenstate condition. Explicit knowledge of the potential operator, other than knowledge of its homogeneity, is not required. In addition, integration of the pointwise equation yields a generalization of the familiar virial theorem. 2 references.
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