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

For the following operator represented in the orthonormal basis {|1>, |2>}

[tex]\hat{M} =

\begin{pmatrix}

2 & i\sqrt{2} \\

-i\sqrt{2 & 2}

\end{pmatrix}

[/tex]

find the eigenvalues and eigenvectors and express them as a function of |1> and |2> normalized.

3. The attempt at a solution

I'm trying to apply what I learned way back in linear algebra. When I solve for the eigenvector coefficients, I end up with a system of 2 variables and 1 equation (alternatively 2 variables and a rank 1 matrix), which gives me (2 - 1) free parameters to set arbitrarily. However back in algebra I used to just pick a variable "gamma" or whatever and leave my eigenvector in terms of it. Now I'm supposed to fix an actual number to it? For what reason and how should I pick my free parameters?

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# Homework Help: Choosing coefficients for eigenvectors.

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