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## Homework Statement

This is quite a long problem, and I have most of it figured out, but I am getting stuck on the very last part of the problem. My problem is I do not understand how to find [itex]\left\langle\psi|a_1\right\rangle[/itex] in the very last line. Is [itex]\left\langle\psi|a_1\right\rangle=(\left\langle a_1|\psi\right\rangle)^*[/itex]

## Homework Equations

In a given basis [itex]\left\langle a^{(i)}\right|[/itex], operators are represented by [itex]A_{i,j}=\left\langle a^{(j)}|A|a^{(i)}\right\rangle[/itex]

## The Attempt at a Solution

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