(adsbygoogle = window.adsbygoogle || []).push({}); Question:

If g(p) can be Taylor expanded in polynomials, then prove that:

[tex] \left[x, g\left(p\right)\right] = i\hbar \frac{dg}{dp} [/tex]

To start, I multiply the wave function [itex] \Psi [/itex] and expand the commutator:

[tex] \left( xg\left(p\right)-g\left(p\right)x \right)\Psi [/tex]

then expand g(p) using Taylor:

[tex] x\left(g\left(a\right) + g'\left(a\right)\left(p-a\right)\right)\Psi + \left(g\left(a\right) + g'\left(a\right)\left(p-a\right)\right)x\Psi [/tex]

Then I'm stuck... I'm nowhere near getting [itex]i\hbar[/itex] or [itex]\frac{dg}{dp}[/itex]

Any help would be appreciated. Thank you!

-Rick

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# Homework Help: Commutator Problem

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