(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi all, I'm having trouble working on the following problem. Any assistance will be greatly appreciated.

Here, the capital letters stand for Position and Momentum operators while the ##x', p'## stand for eigenvalues.

2. Relevant equations

3. The attempt at a solution

a) and b)

It seems that a) and b) can be written in the form of

$$e^{\frac{i}{\hbar}x'P}e^{\frac{i}{\hbar}p'X}$$

which I can then express in the form of the BCH identity

$$e^{\frac{i}{\hbar}x'P}e^{\frac{i}{\hbar}p'X} = e^{\frac{i}{\hbar}x'P + \frac{i}{\hbar}p'X + \frac{i}{2\hbar}x'p' + 0 + O'}$$

where I denote the other terms by ##O'##. If ##O' = 0##, I obtain b), if ##O' = \frac{i}{2\hbar}x'p' ##, I get a). Is this what the question was getting at? It does seem too convenient.

c)

I'm not too sure where to start with this one.

Thanks in advance for any help!

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# Special Cases of the BCH Identity

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