- #1
wdlang
- 307
- 0
given two arbitrary states of a spin of 1/2
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
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
Last edited: