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$-k^2f''(x)=(E^2-V(x))f(x)$ I have checked for many V(x) that the set of solutions to this differential equation are complete and have an orthogonal basis set, is this always true for all V(x)?

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    Complete means every square integrable function can be written as int a(k)z(k,x) dk , where z(k,x) is all solutions parametrized by k, and a(k) is allowed to be a delta function2012-12-28
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    orthogonal means int z(k,x)*z(b,x) dx vanishes when b not equal to k2012-12-28

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