April 2nd, 2013, 5:42 pm
Yes I can, but the proof is a bit long:By separation of variables I have 1. which is easy to solve, and 2. problem 2 can be rewritten as self-adjoint form:which is an eigenvalue / eigenfunction problem, and then we can apply regular Sturm Liouville theorem, the eigenvalues / eigenfunctions are Since probability density has to be positive, of all the eigenfunctions only is positive and never changes sign. So it is the only valid solution to the problem, and its eigenvalue is also the only solution.