Operators and Commutators help

[TIGERHULL]

Hi, I have this question 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 :)

 

[Timo]

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

 

[TIGERHULL]

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

 

[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).