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Newbie says Hi
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Homework Statement
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?
Homework Equations
[tex] \hat{x} = x [/tex]
[tex] \hat{p} = -i \hbar \frac{\partial}{\partial x} [/tex]
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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