(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

With knowledge of the orthogonality conditions for eigenfunctions with discrete eigenvalues, determine the orthonormal set for eigenfunctions with continuous eigenvalues. Use the definition of completeness to show that | a(k) |^2 = 1.

2. The attempt at a solution

The first step is:

http://img55.imageshack.us/img55/5229/81115215vg1.jpg [Broken]

http://g.imageshack.us/img55/81115215vg1.jpg/1/ [Broken]

Since the integral is only equal to 0 when k' = k. (The same condition as the kronecker delta.)

Next:

http://img352.imageshack.us/img352/9519/94213081to0.jpg [Broken]

http://g.imageshack.us/img352/94213081to0.jpg/1/ [Broken]

After here I get a bit lost, even though I think this is almost the solution. My work differs from the course notes and a QM book I've looked through. They both have an integration with respect to k for the RHS, not x.

Any pointers would be greatly appreciated.

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# Homework Help: Orthogonality of eigenfunctions with continuous eigenvalues

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