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\[S _{y}\] is y component of s & s is spin.solve it in two dimension

i know what do that. but final answer has not matched with text

I was going to just take a wild guess, but really, I have no idea :P

First, can you write out \( S_y \) explicitly?

Whatever it is, write it out explicitly.

Sy= \[\left[\begin{matrix}h'/2 & -ih'/2 \\ih'/2 & h'/2\end{matrix}\right]\] h'=h/2pi

is operation

yes know this but final answer don't match with text

What did you find for eigenvalues?

I have from that definition of Sy, that the eigenvalues are 0 and h'

eigen value is match eigenvector... i didn't find

your eigenvalues is zero?

eigenvalue is +h'/2&-h'/2

this book is solution of Introduction to quantum mechanics by david.-j griffiths

You gave the wrong \( S_y \). Notice the matrix in the book has zeros along the diagonal, unlike the matrix you typed above.

compare your Sy with mine

so...

eigenvalue is ok thanx,now eigenvectors

i knew method but final answer don't matched can you give me details of solution ?