$-k^2f''(x)=(E^2-V(x))f(x)$ 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)?
Time Independent Schrodinger equation
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ordinary-differential-equations
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0Complete 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 function – 2012-12-28
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0orthogonal means int z(k,x)*z(b,x) dx vanishes when b not equal to k – 2012-12-28