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Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Journal Article

W. K. B. Approximation and Scaling

K. Banerjee
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 363, No. 1712 (Nov. 1, 1978), pp. 147-151
Published by: Royal Society
https://www.jstor.org/stable/79720
Page Count: 5

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Topics: Approximation, Eigenvalues, Virial theorem, Polynomials, Oscillators
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W. K. B. Approximation and Scaling
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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.
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1978 Royal Society