## Problem with Eigenkets

1. The problem statement, all variables and given/known data
Show that if an operator A has an eigenket |a> to eigenvalue a then
the adjoint operator A† has an eigenbra <a*| to eigenvalue a*. How
is <a*| related to |a>?

2. Relevant equations
A|a> = |a>a
| >† = < |

3. The attempt at a solution
I actually have no clue where to start this question. I am guessing it has something to do with A† would have an eigenket of |a>†. But I am unsure if this is correct at all.
Would anyone be able to help me get started.

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 Quote by ConeOfIce 1. The problem statement, all variables and given/known data Show that if an operator A has an eigenket |a> to eigenvalue a then the adjoint operator A† has an eigenbra ? 2. Relevant equations A|a> = |a>a | >† = < | 3. The attempt at a solution I actually have no clue where to start this question. I am guessing it has something to do with A† would have an eigenket of |a>†. But I am unsure if this is correct at all. Would anyone be able to help me get started.
Take the dagger of (A |a>) This must be equal to the dagger of (a |a>).

 Quote by nrqed Take the dagger of (A |a>) This must be equal to the dagger of (a |a>).
Ok, I do this. And I also took the dagge of both sides of the equation. So I got
(A|a>)^(dagger) = (|a>a)^dagger which gets

<a|A* = a*<a|.

And using your statement form above I then do
A*<a| = a|a> .
How does this get me any closer to the answer?

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## Problem with Eigenkets

Why would a*=a ??

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