(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[A[itex]^{+}[/itex]A]=1

A|a>=[itex]\sqrt{a}[/itex]|a-1>

A[itex]^{+}[/itex]|a>=[itex]\sqrt{a+1}[/itex]|a+1>

<a'|a>=[itex]\delta_{a'}_{a}[/itex]

2. Relevant equations

what is

1 <a|A|a+1>

4. <a+1|A[itex]^{+}[/itex]|a>

3. <a|A[itex]^{+}[/itex]A|a>

4. <a|AA[itex]^{+}[/itex]|a>

3. The attempt at a solution

1. <a|A|a+1> =<a|[itex]\sqrt{a+1}[/itex]|a+1-1>=[itex]\sqrt{a+1}[/itex]<a|a>

since a=a and since its the Knocker delta it equals 1 so it equals

[itex]\sqrt{a+1}[/itex]

2.<a+1|A[itex]^{+}[/itex]|a>=<a+1|[itex]\sqrt{a+1}[/itex]|a+1>=

[itex]\sqrt{a+1}[/itex]<a+1|a+1>

since a+1=a+1 and since its the Knocker delta it equals 1 so it equals

[itex]\sqrt{a+1}[/itex]

<a|A[itex]^{+}[/itex]A|a> this is where i am having problems

(<a|A[itex]^{+}[/itex])*(A|a>)= A[itex]^{+}[/itex]A<a|a>=1 is this right

the same is for part 4

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# Homework Help: Dirac notation with operators

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