If I've learned one thing in my graduation so far is that I must assume when I finish my calculations that I am probably wrong and start doing "sanity" tests. I am very good at doing foolish mistakes. I am taking a course on quantum mechanics at undergraduate level. We have worked at the first moment in finite-dimensional Hilbert space problems and on those I mostly had the instinct of checking everything: I could check determinants, trace, linear dependency, normalization.
Now we are dealing with infinite dimensional problems and I think I know the theory mostly but I can't get good at the calculation procedures. Specially when it comes to the boundary problems solutions, for example, when it comes to determine the reflective coefficient in a scattering problems or even at what sort of algebraic manipulations I have to do to extract a transcedental equation which will lead me to the discrete energy levels (cf. Cohen-Tannoudji ch. 1 complement H1). Most of the times I don't know if I'm proceeding in the "simple" (or even right) way. I really wanted to improve on that but I do not know what sort of tests or intuition I can have on those equations to check where I'm going and if they make sense!