Answer to Question #135469 in Physical Chemistry for taylor

Question

Determine whether the following function are suitable as wavefunctions:
F(x) = 0 for x < 1;
= 1/x for x > 1;
= 0 for x > 1000.

Answer 1

For the following basis of functions (Y2p-1, Y2p0 , and Y2p+1), construct the matrix representation of the Lx operator (use the ladder operator representation of Lx). Verify that the matrix is hermitian. Find the eigenvalues and corresponding eigenvectors. Normalize the eigenfunctions and verify that they are orthogonal. Y2p-1 = 1 8p1/2 è æ ø Zö a 5/2 re-zr/2a Sinq e-if Y2po = 1 p1/2 è æ ø Zö 2a 5/2 re-zr/2a Cosq Y2p1 = 1 8p1/2 è æ ø Zö a 5/2 re-zr/2a Sinq eif

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