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## Summary:

- If we chose Z axis when defining electron spin states, how do we choose X and Y directions then?

## Main Question or Discussion Point

For a 1/2 spin particle, every pure spin state may be represented as a superposition of two states of spin parallel to some arbitrary Z axis.

(Upd) Particularly:

$$|\uparrow_{x}>=\frac{1}{\sqrt{2}}(|\uparrow_{z}>+|\downarrow_{z}>)$$

I then wonder, if we chose the Z axis, how the X axis should be chosen to make the above equality true?

(Upd) Particularly:

$$|\uparrow_{x}>=\frac{1}{\sqrt{2}}(|\uparrow_{z}>+|\downarrow_{z}>)$$

I then wonder, if we chose the Z axis, how the X axis should be chosen to make the above equality true?

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