- #1

Sparky_

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I have a question about a statement made on a YouTube physics lecture

I was (am) working through chapter 4 section 4 (4.4) - “Spin” of Griffiths. (only because I own this book ) I found the YouTube lectures by searching for phrases like “quantum Griffiths online lectures”. One of the search results was Brant Carlson’s YouTube channel. He is a professor at Carthage college. His quantum lectures are on his channel. He uses Griffiths. I am following the parallel between angular momentum and spin and ladder operators. The mathematics is not an issue, matrix algebra or just algebra.

__Within his lecture on spin he states at 21:10 (direct quote) “If I combine 2 states with definite z angular momentum in this very specific superposition, I end up with this state of definite x angular momentum”__**My question or confusion is this is his bringing in a statement about “z”**. Within the work leading up to this statement, z was never mentioned nor used, meaning it was all x and y within the work:

$$\ S_x |\psi\rangle = \lambda |\psi\rangle \\

\frac {\hbar } {2} \begin{pmatrix}

0 & 1 \\

1 & 0

\end{pmatrix} \begin{pmatrix}

x \\

y \end{pmatrix} = \lambda \begin{pmatrix}

x \\

y \end{pmatrix} \\ ... \\

\lambda = \pm \frac{\hbar}{2} \\ ... \\

\begin{pmatrix}

\frac{\mp\hbar}{2} & \frac{\hbar}{2} \\

\frac{\hbar}{2} & \frac{\mp\hbar}{2}

\end{pmatrix} \begin{pmatrix}

x \\

y \end{pmatrix} = 0 \\

x = \pm y\\

normalized \\

\begin{pmatrix}

\frac{1}{\sqrt{2}} \\

\frac{1}{\sqrt{2}} \end{pmatrix}\\

\chi_+ =

\begin{pmatrix}

\frac{1}{\sqrt{2}} \\

\frac{1}{\sqrt{2}} \end{pmatrix} \\

\chi_- =

\begin{pmatrix}

\frac{1}{\sqrt{2}} \\

-\frac{1}{\sqrt{2}} \end{pmatrix} \\$$

His material before his statement was the above, all dealing with x and y eigenvalues and so forth. I do not understand his statement, "

**"**

__“If I combine 2 states with definite z angular momentum in this very specific superposition, I end up with this state of definite x angular momentum”__Thanks

Sparky_