Table of Contents

Calculating Inner Products

The Prompt

For the generic bra vector $<v|$ and ket vector $|w>$ we can compute the inner product. Write it down.

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With vectors

$$ \vert 1\rangle =\left(\begin{array}{c} 1\\ 0\\ 0\\ \end{array}\right) $$ $$ \vert r\rangle =\left(\begin{array}{c} 0\\ 1\\ 1\\ \end{array}\right) $$

Compute $\langle 1\vert r\rangle$ and $\langle r\vert 1\rangle$.

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Compute $\langle v_{1}\vert v_{2}\rangle$ for eigenvectors

$$ \vert v_{1}\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ 1\\ \end{array}\right) $$

$$ \vert v_{2}\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ -1\\ \end{array}\right) $$

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Context

This SWBQ

Wrap Up