1 nevertheless the theorem does allow us certain

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Unformatted text preview: ctions.1 Nevertheless, the theorem does allow us certain shortcuts in calculations. 1 The extension of this to certain approximate solutions is due to R. P. Feynman and H. Hellmann. See Problem 10 in Chapter 14. W-35 W-36 Supplement 8-A A Useful Theorem Consider, for example, the one-dimensional simple harmonic oscillator, for which the Hamiltonian is p2 2m H 1m 2 2 x 2 (8A-5) The eigenvalues are known to be En 1 2 (n (8A-6) ) If we differentiate En with respect to , and if we note that H m x2 we can immediately make the identification 1 2 (n ) x2 m n or x2 En m2 1 2 n m n (8A-7) Examples of relevance to the hydrogen atom are of particular interest. In the Hami...
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