I am studying QM by myself. I got a quite confusing problem which annoying me for a certain time. Well, this question is about the angular momentum opeator Lx, Ly and Lz. The matrix form for these operatore are given, so by solving the corresponding secular equation, it is easy to find the corresponding eigenvalues and eigenvectors. Here, Lz is given in a diagonalized form, so one can directly obtain the eigenvalues by reading the diagonal elements. Let's say the eigenvalues for Lz is a, b and c. And the corresponding eigenvector are(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\left(

\begin{matrix}

1 \\ 0 \\ 0

\end{matrix}

\right), \qquad

\left(

\begin{matrix}

0 \\ 1 \\ 0

\end{matrix}

\right),\qquad

\left(

\begin{matrix}

0 \\ 0 \\ 1

\end{matrix}

\right)

[/tex]

But I got a question "To find the eigenvectors of Lx in the Lz basis", I have no idea what does it mean? Since we already know the form of Lx operator, what can't we just solve the secular equation to find the eigenvectors? What is the significance of written the eigenvectors of Lx in Lz basis?

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# What does it mean to find eigenvectors of some operator in some basis?

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