- #1
FarticleFysics
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I'm trying to practice some operator algebra..
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.
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.