Comment Re:what happens when the elecron is "entangled" .. (Score 1) 157
|up, down> + |down, up> is not an eigenstate of the spin flip operator. Correct.
However, that doesn't mean you can't apply the spin-flip operator to it. I don't know how to explain it in more detail, other than to try and give an experimental realization, which I don't think is what you're looking for.
Perhaps this will make more sense... let's work in "vector notation"...
define |up, up> = (1, 0, 0, 0)
|up, down> = (0, 1, 0, 0)
|down, up> = (0, 0, 1, 0)
|down, down> = (0, 0, 0, 1)
The spin flip operator for the first electron can now be written in matrix form as
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0
Since this matrix is unitary (see http://mathworld.wolfram.com/UnitaryMatrix.html), then this is a valid time-evolution operator in quantum mechanics.
I guess I really haven't said anything new here, so I doubt that actually clarifies anything. But I'm not sure what it is you don't understand.
However, that doesn't mean you can't apply the spin-flip operator to it. I don't know how to explain it in more detail, other than to try and give an experimental realization, which I don't think is what you're looking for.
Perhaps this will make more sense... let's work in "vector notation"...
define |up, up> = (1, 0, 0, 0)
|up, down> = (0, 1, 0, 0)
|down, up> = (0, 0, 1, 0)
|down, down> = (0, 0, 0, 1)
The spin flip operator for the first electron can now be written in matrix form as
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0
Since this matrix is unitary (see http://mathworld.wolfram.com/UnitaryMatrix.html), then this is a valid time-evolution operator in quantum mechanics.
I guess I really haven't said anything new here, so I doubt that actually clarifies anything. But I'm not sure what it is you don't understand.
