Suppose Âgn = (ngn. Let the eigenfunctions gn be expanded in terms of the complete orthonormal set {(i} according to

Substitute this expansion into

Multiply by (*i, integrate over all space, and show that the set of equations

For i = 1, 2, 3, ( ( ( is obtained, where

This set of equations has the same form as the set (8.53) with Sik = (ik. Thus, just as the W values and the coefficients ck in (8.53) with Sik = (ik can be found by finding the eigenvalues and eigenvectors of the H matrix, the eigenvalues an of  and the expansion coefficients ck(n) k of the eigenfunctions gn of  can be found by finding the eigenvalues an and eigenvectors c(n) of the matrix A, whose elements are Aik.

Transcribed Image Text:

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