- #1

- 19

- 0

## 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.