- #1
umagongdi
- 19
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Homework Statement
Suppose that the commutator between two Hermitian operators â and [tex]\hat{}b[/tex] is [â,[tex]\hat{}b[/tex]]=λ, where λ is a complex number. Show that the real part of λ must vanish.
Homework Equations
Let
A=â
B=[tex]\hat{}b[/tex]
The Attempt at a Solution
AΨ=aΨ BΨ=bΨ
ABΨ=AbΨ=bAΨ=baΨ=abΨ=aBΨ=BaΨ=BAΨ
AB=BA
[A,B]=0
This can't be the answer since we need the complex part.
or
[A,B]Ψ=ABΨ-BAΨ=Re(λ)Ψ+Im(λ)Ψ, i have no idea how to get rid of Re(λ). Any ideas? Thanks.