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

Find the commutator [tex]

\left[\hat{p_{x}},\hat{p_{y}}\right]

[/tex]

2. Relevant equations

[tex] \hat{p_{x}}=\frac{\hbar}{i}\frac{\partial}{\partial x} [/tex]

[tex] \hat{p_{y}}=\frac{\hbar}{i}\frac{\partial}{\partial y} [/tex]

3. The attempt at a solution

[tex][\hat{p}_{x}, \hat{p}_{y}]=\hat{p}_{x}\hat{p}_{y}-\hat{p}_{y}\hat{p}_{x}[/tex]

[tex]=\frac{\hbar}{i}\frac{\partial}{\partial x}\frac{\hbar}{i}\frac{\partial}{\partial y}-\frac{\hbar}{i}\frac{\partial}{\partial y}\frac{\hbar}{i}\frac{\partial}{\partial x}[/tex]

[tex]=(\frac{\hbar}{i})^2\frac{\partial^2}{\partial x\partial y}-(\frac{\hbar}{i})^2\frac{\partial^2}{\partial y\partial x}[/tex]

Is this the correct commutator? I don't know what else I can do to further complete this. Any help is appreciated.

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# Homework Help: Commutator problem with momentum operators

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