Operator Equation Msg Deleted: Solving Info Issues

Thread starter JohanL
Start date Sep 12, 2006
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Operator

Sep 12, 2006

JohanL

message deleted

Last edited: Sep 13, 2006

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Sep 12, 2006

HallsofIvy

Science Advisor

Homework Helper

Proof by induction (on m) should work.

If m= 1, then
a^{m}(a\dagger)^{m}= aa\dagger= n+1
which is the correct formula.

Now, assume that, for some k,
a^{k}(a\dagger)^{k}=(n+1)(n+2)...(n+k)
and look at
a^{k+1}(a\dagger)^{k+1}= a(a^{k}(a\dagger)^k) a\dagger
= a((n+1)(n+2)...(n+k))a\dagger
and apply the commutativity relation to that.

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