Abstract
It is shown that the W. K. B. eigenvalues and eigenfunctions satisfy the Hellmann-Feynman theorem and the virial theorem. As a consequence the scaling behaviour of the exact eigenvalues with respect to the parameters in the Hamiltonian is retained in the W. K. B. approximation for the polynomial potentials. Hypervirial relations of certain lower orders are also satisfied by the W. K. B. approximants.
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