I'm trying to practice some operator algebra..(adsbygoogle = window.adsbygoogle || []).push({});

Solve [H,x] where H is the Hamiltonian operator, x is position operator, and assuming one dimensional potential energy, U(x).

I know the commutator comes out as -ih_bar(p_op)/m

Here is my work so far.

[H,x] = Hx - xH

note: H = [ -ih_bar(p/2m) + U(x) ]

so.. plug it in.. [ -ih_bar(p/2m) + U(x) ] x - x [ -ih_bar(p/2m) + U(x) ]

( x U(x) and -x U(x) cancel)

now.. -(ih_bar/2m)(p x) + (ih_bar/2m)(x p)

-(ih_bar/2m)[ p x - x p ]

x and p are both operators.. so I know they don't cancel.. I'm kind of lost at this point.

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# Solving [H,x] =

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