Quantum entanglement and potential wells

[satyesu]

I've read that two electrons can become entangled in a "potential well," which is a point where potential energy is lowest compared to its surroundings. Is this correct? What does this have to do with entangling particles?

 

[Nugatory]

I've read that two electrons can become entangled in a "potential well," which is a point where potential energy is lowest compared to its surroundings. Is this correct? What does this have to do with entangling particles?

Entanglement happens pretty much whenever two particles interact with one another. Two electrons in a potential well will be close enough to one another to interact, so it's easy to entangle them.

 

[vanhees71]

Elekctrons are always entangled, because they are indistinguishable fermions, i.e., the state vectors are never product states but antisymmetrized product states,
$$|\Psi \rangle=|\psi_1,\psi_2 \rangle-|\psi_2, \psi_1 \rangle,$$
or superpositions of such antisymmetrized product states.

 

[satyesu]

Elekctrons are always entangled, because they are indistinguishable fermions, i.e., the state vectors are never product states but antisymmetrized product states,
$$|\Psi \rangle=|\psi_1,\psi_2 \rangle-|\psi_2, \psi_1 \rangle,$$
or superpositions of such antisymmetrized product states.

Whoa, whoa, whoa. That lingo is above my head so far. What are state vectors and product states, and if e-'s can't be product states at all how can they be "asymmetrized" product states? And, Nugatory, thank you very much.

 

[vanhees71]

It's impossible to understand what entanglement is without these fundamental mathematical notions. For a nice introduction to what QT really is, see

https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

 

[satyesu]

I think my library has that! But I'll probably have to reserve it. Thanks, though!