There is something I'm struggling with and I can't seem to find the problem.(adsbygoogle = window.adsbygoogle || []).push({});

We have the Z spinbase with:

z = (1/sqrt(2))² <BRA|*(|s_z,+> + |s_z,->)

which gives following z matrix:

1 0

0 1

and we have for X:

|s_x, +> = 1/sqrt(2) |s_z,+> + |s_z,->)

|s_x, -> = 1/sqrt(2) |s_z,+> - |s_z,->)

Now I have a problem with making the x matrix.

this one is equal to

0 1

1 0

but this doesn't fit with the base above?

for example the first component:

<s_x,+|s_x,+> = 1/2 {<s_z,+|s_z,+> + <s_z,+|s_z,-> + <s_z,-|s_z,+> + <s_z,-|s_z,-> }

<s_z,+|s_z,+> = <s_z,-|s_z,-> = 1

<s_z,+|s_z,-> = <s_z,-|s_z,+> = 0 because of orthogonality,

so we get that <s_x,+|s_x,+> = 1 instead of 0?

What do I do wrong?

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# Spin base transformation

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