Operators and Commutators help

1. Oct 18, 2011

TIGERHULL

Hi, I have this quesiton for a problem sheet:

Use the unit operator to show that a Hermitian operator A can be written in terms of its orthonormal eigenstates ln> and real eigenvalues a as :

A=(sum of) ln>a<nl

and hence deduce by induction that A^k = (sum of) ln>a^k<nl

I have no idea where to begin and was wondering if someone could give me some pointers and help me work through it. Also, sorry about my notation

Thanks :)

2. Oct 18, 2011

Timo

You are probably assumed to know that $$1 = \sum_n |n\rangle \langle n|$$, where 1 means the unit operator.

3. Oct 18, 2011

TIGERHULL

Yes we are, sorry it says that as well. Any pointers on where to begin still?

4. Oct 18, 2011

Timo

Sure, but I think it's rather obvious as the question already says is: A = 1A = A1 (that's the definition of the unity operator, btw).