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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!

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    $\begingroup$ One of the obvious sanity checks on quantum systems is to take the classical limit, although this is not always straightforward. Another would be to compare your solution to wave optics. I can't help you much with transcendental equations however. $\endgroup$ – By Symmetry May 26 '17 at 15:40

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