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4

To answer the question, over and above the errors noted in the other answer the integral is just not well defined - it is infinite. There are two ways to see this The "common sense" method. Consider $$\int^\infty_{-\infty} \left[ A\sin(kx) + B \cos(kx)\right]^2dx$$ The quantity under the integral is positive semi-definite - it is always greater ...

1

Your attempt has multiple issues, most of which are very basic. The first issue that I noticed was how you expanded and simplified your integral. \begin{align} \int^\infty_{-\infty}[A^2\sin^2(kx) &+ AB\sin(kx)\cos(kx) \\ &+ AB\cos(kx)\sin(kx) +B^2\cos^2(kx)]\mathrm dx = 1 \tag{1} \end{align} Since, $\sin^2 x + \cos^2 x = 1$, \implies \int^\...

3

This is deeper discussed in Rate Constant Units and Eyring Equation, but I am going to post a very short take-home message here. First, the three assumptions you have cited are not complete. They completely gloss over the most important one, i.e. nuclear and electron motion can be separated, energies (translation, vibration, rotation) can be treated ...

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