The discussion revolves around the concept of quantum entanglement, particularly in the context of electrons within a potential well. Participants explore the relationship between potential wells and the conditions under which electrons can become entangled, as well as the implications of their indistinguishable nature as fermions.
There is no consensus on the nature of entanglement in relation to potential wells, with differing views on whether electrons can be considered always entangled and the implications of their indistinguishability. The discussion remains unresolved regarding the clarity of the concepts involved.
Participants express varying levels of understanding regarding the mathematical framework of quantum mechanics, indicating potential limitations in grasping the concepts discussed. The discussion also reflects uncertainty about the definitions and implications of terms like state vectors and product states.
This discussion may be of interest to those exploring quantum mechanics, particularly in relation to quantum entanglement and the behavior of fermions.
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.satyesu said: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?
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 said: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.