From: *Brent Meeker* <[email protected] <mailto:[email protected]>>
On 4/19/2018 9:10 PM, [email protected]
<mailto:[email protected]> wrote:
On Friday, April 20, 2018 at 1:18:32 AM UTC, Bruce wrote:
Those are not generalized basis vectors: they are eigenfunctions
of the spin projection operator in a particular basis. The
singlet state is not a superposition of vectors from different bases.
*Which particular basis; the UP/DN basis? Does this mean the two
tensor product states defining the singlet state don't interfere with
each other? *
No.
*Can you have superpositions of vectors from different bases? I don't
think so/. /AG *
Sure you can. It just makes the math complicated.
I don't think it makes much sense to form a superposition of vectors
from two different bases. Say you take one eigenvector from the x-basis,
and one from the y-basis. All you have actually done is form a weighted
superposition of vectors -- which can be expressed in either basis.
Remember, superpositions are just vectors in the Hilbert space, so
according to normal linear algebra, they can be expanded in terms of any
complete set of basis vectors. But it makes little sense to try
expanding in two different bases simultaneously. Whatever that might
give, it is still nothing more than a vector in the space, which can be
represented in any basis you choose.
Bruce
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