Calculating Spin Operators for Spin 1/2 Systems

[aliveinmoscow]

1. 1) Consider a spin 1/2 system...

a) write expressions for the operators Sx Sy Sz in the basis composed of eigenkets of Sz
b) Write eigenvalues of Sx Sy Sz
c) Write eigenvectors of Sx and Sy in this basis

2) Write a matric corresponding to the operator S_ in the basis composed of the eigenkets of the operator Sx, |Sx;+->



2. Homework Equations : None



3. the results i have so far are:

1 = |+> <+|+|-><-|
Sz=h(bar)/2[|+> <+|+|-><-|]

 

[bdforbes]

Where you write <+|+|->, what does the center + refer to? Usually an operator is located in that position.

For a start, you should write out the eigenkets of S_z. What do S_x, S_y and S_z do when acted on these eigenkets?