- #1

Niles

- 1,868

- 0

## Homework Statement

Hi

Please take a look at the following equality found in my book:

[tex]

\left| \mu \right\rangle = \sum\limits_v {\left| v \right\rangle \left\langle {v}

\mathrel{\left | {\vphantom {v \mu }}

\right. \kern-\nulldelimiterspace}

{\mu } \right\rangle } = \sum\limits_v {\left\langle {\mu }

\mathrel{\left | {\vphantom {\mu v}}

\right. \kern-\nulldelimiterspace}

{v} \right\rangle ^* \left| v \right\rangle }

[/tex]

The asterix denotes complex conjugation. I cannot see why the second equality holds, since

[tex]

\sum\limits_v {\left\langle {\mu }

\mathrel{\left | {\vphantom {\mu v}}

\right. \kern-\nulldelimiterspace}

{v} \right\rangle ^* \left| v \right\rangle } = \sum\limits_v {\left\langle {v}

\mathrel{\left | {\vphantom {v \mu }}

\right. \kern-\nulldelimiterspace}

{\mu } \right\rangle \left| v \right\rangle } \ne \sum\limits_v {\left| v \right\rangle \left\langle {v}

\mathrel{\left | {\vphantom {v \mu }}

\right. \kern-\nulldelimiterspace}

{\mu } \right\rangle }

[/tex]

What am I missing here?

Best,

Niles.