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

Determine [tex]\left[\hat{x},\hat{H}\right][/tex]

2. Relevant equations

3. The attempt at a solution

[tex]=x\left(-\frac{\hbar^2}{2m}\frac{\delta^2}{\delta{x^2}}+V\right)\Psi-\left(-\frac{\hbar^2}{2m}\frac{\delta^2}{\delta{x^2}}+V\right)x\psi[/tex]

[tex]x\left(-\frac{\hbar^2}{2m}\frac{{\delta^2}\psi}{\delta{x^2}}+V\psi\right)+\frac{\hbar^2}{2m}\frac{{\delta^2}(x\psi)}{\delta{x^2}}-Vx\psi[/tex]

[tex]x\left(-\frac{\hbar^2}{2m}\frac{{\delta^2}}{\delta{x^2}}\right)+\frac{\hbar^2}{2m}\frac{\delta}{\delta{x}}\left(\psi+x\frac{\delta\psi}{\delta{x}}\right)[/tex]

How do you get from the 2nd line to the 3rd? is it an identity of partial differentials? can someone explain how to split the d squared term into two separate parts?

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# Homework Help: Commutator maths problem

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