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A simple question about tuesday's discussion. When solving for the eigenvector for the second and third eigenstate, I am getting

<math>|s_2\rangle = |s_3\rangle = \begin{bmatrix} 0
1
1 \end{bmatrix}</math>

but the answers we arrived at in discussion were

<math>|s_2\rangle = \begin{bmatrix} 0
1
0 \end{bmatrix}</math> and <math>|s_3\rangle = \begin{bmatrix} 0
0
1 \end{bmatrix}</math>

So what am I missing here? Thanks.

Spherical coord. are helpful when dealing with mostly spherical volumes – but if we were only interested in volumes… for the problems we're dealing with, would it really change much to approximate the volume as a small box, not a sphere? We've not really dealt with the different spin and momentum volumes l,m, etc so obviously not there.. but if we weren't concerned with r, couldn't we still keep the coordinates rectangular?

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