Operation algebra: prove [A,f(A)]=0

Thread starter itai
Start date Dec 10, 2010
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Algebra

AI Thread Summary

The discussion focuses on proving that the commutator [A, f(A)] equals zero for a given operator A. The equation is defined as [A, f(A)] = Af(A) - f(A)A. Participants express uncertainty about how to proceed from the equation, particularly regarding the implications of f(A)A equating to Af(A). It is noted that if f(z) is analytical, it can be expressed as a power series. The conversation emphasizes the need for a deeper understanding of operator algebra to resolve the proof.

Dec 10, 2010

itai

Homework Statement

given an opeator A, prove that the commutator satisfies:
[A,f(A)]=0

Homework Equations

[A,f(A)]=Af(A)-f(A)A

The Attempt at a Solution

I don't know how to continue from Af(A)-f(A)A=0
I can't just say that f(A)A=Af(A).
Any ideas?

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Dec 10, 2010

quZz

if f(z) is analytical then you have f(z) = f0 + f1 z + f2 z² + ...

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