On 4/19/2018 9:45 PM, Bruce Kellett wrote:
From: *Brent Meeker* <meeke...@verizon.net>
On 4/19/2018 9:10 PM, agrayson2...@gmail.com
<mailto:agrayson2...@gmail.com> 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.
Or some third 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.
I assumed you would expand one, say the one from the x-basis, in the
basis the other, the y-basis, in order to have them both expressed in
the same basis. Or expand them both in some third basis. I wouldn't
expand them in two different bases. I don't know what would be the
point of that.
Whatever that might give, it is still nothing more than a vector in
the space, which can be represented in any basis you choose.
Right.
Brent
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