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

I've just initiated a self-study on quantum mechanics and am in need of a little help.

The position and momentum operators do not commute. According to my book which attemps to demonstrate this property,

(1) [tex]\hat{p} \hat{x} \psi = \hat{p} x \psi = -i \hbar \frac{\partial}{\partial x}(x \psi)[/tex]

OK, so far I was following. I'm not understaing how they get to this next equation from the previous one...

(2) [tex] = -i \hbar \left( \psi + x \frac{\partial \psi}{\partial x}\right)[/tex]

To be more precise, where did the second psi symbol come from and where did the + symbol come from in equation 2?

2. Relevant equations

[tex] \hat{x} = x [/tex]

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

3. The attempt at a solution

When I attempt to multiply the momentum and position operators, I get:

(3) [tex] \hat{p} \hat{x} \psi = \hat{p} x \psi = \left( -i \hbar \frac{\partial}{\partial x} \right) x \psi [/tex]

But how do I go from equation 3 and arrive at equation 2? Or can I?

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# Homework Help: Commutation relation of the position and momentum operators

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