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Unformatted text preview: Supplement 8-A A Useful Theorem
The following useful result appears in Pauli’s 1930 “Handbuch Article on Quantum Theory”:
Consider eigenvalues and eigenfunctions of a Hamiltonian that depends on some parameter—for example, the mass of the electron, or the charge of the electron, or any other
parameter that may appear in more complicated problems. The Schrödinger eigenvalue
equation may then be written with the parameter explicitly indicated as,
H( )un(r, ) E( )un(r, ) (8A-1) It follows that with the eigenfunctions normalized to unity,
d 3ru*(r, )un(r, )
n 1 (8A-2) that
d 3ru*(r, )...
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This document was uploaded on 10/31/2011.
- Spring '09