I have already broken a PDE problem into an ODE problem with the method of separation of variables.
But the right boundary locates at infinity.
If the right boundary locates at a specific point, I think I can get an orthonormal solution system.
But I don't know how to get the eigenvalues by the right boundary at infinity.
Please have a look at this issue. Thanks.
eq10 = p1[x] == \[Lambda]*Dp (p1^\[Prime]\[Prime])[x] // Simplify //
eq11 = Derivative[p1][lh] == \[Alpha]1 p1[lh] // Simplify // Normal
eq12 = Derivative[p1][\[Infinity]] == 0 // Simplify // Normal