given two arbitrary states of a spin of 1/2(adsbygoogle = window.adsbygoogle || []).push({});

we can always find a rotation to link these two states

however, given two arbitrary states of a spin of 1

this is not so

for example, (0,1,0) and (1,0,0) can not be linked by a rotation

the former has vanishing expectations of sx, sy, sz

so in rotation, the expectations values are always vanishing

<sx>^2+<sy>^2+<sz>^2=0

however, the latter has <sx>=<sy>=0, <sz>=1;

in rotation, <sx>^2+<sy>^2+<sz>^2=1

this indicates the two can not be linked by a rotation

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# Why two s=1/2 states can be linked by a rotation, but not two s=1 states?

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