What Are the Eigenvalues of Entangled Electron Spins?

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Discussion Overview

The discussion revolves around the eigenvalues and eigenstates of entangled electron spins, particularly focusing on the differences between entangled and unentangled systems. Participants explore the implications of measurement in quantum mechanics and the role of various operators, such as the Hamiltonian and position operator, in determining these properties.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes a list of eigenvalues for an entangled pair of electrons but questions how measurement yields individual eigenvalues rather than combined states.
  • Another participant points out the confusion between eigenstates and eigenvalues and emphasizes the need to specify the operator in question.
  • There is a discussion about the quantum state of entangled versus unentangled systems, with a participant questioning how they differ despite similar measurement outcomes.
  • Several participants repeatedly ask for clarification on which Hamiltonian is being referenced, indicating a lack of specificity in the original questions.
  • A participant mentions that the position operator acts on a single particle state space, leading to a discussion about the eigenstates being the same as in the single particle case.
  • Another participant inquires about other operators that act solely on a single particle state space, seeking to expand the discussion beyond the position operator.

Areas of Agreement / Disagreement

Participants express differing views on the nature of eigenvalues and eigenstates in the context of entangled systems. There is no consensus on the specifics of the Hamiltonian or the implications of measurement in entangled versus unentangled states.

Contextual Notes

Participants have not clearly defined the Hamiltonian or the specific operators being discussed, leading to ambiguities in the analysis. The discussion also reflects varying levels of understanding regarding the relationship between quantum states and measurement outcomes.

lucas_
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Lets' say you have an entangled pair of electrons with spin up and spin down. What is its eigenvalues.. is it..

Eigenvalue 1: Electron A with spin up
Eigenvalue 2: Electron A with spin down
Eigenvalue 3: Electron B with spin up
Eigenvalue 4: Electron B with spin down

But it's supposed to be entangled.. how come during measurement you don't get eigenvalues of..

Eigenvalue 1: Electron A + Electron B spin up
Eigenvalue 1: Electron A + Electron B spin down
?
 
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You're confusing eigenstates with eigenvalues. And you don't specify which operator they are supposed to belong to.
 
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Jazzdude said:
You're confusing eigenstates with eigenvalues. And you don't specify which operator they are supposed to belong to.

Hamiltonian operators on position and spin. I want to understand the quantum state of entangled system versus unentangled system. In entangled system, the quantum state doesn't just contain particle A or particle B but they are entangled.. yet when you measured them.. they are in particle A or B.. so how do they differ when end results in the same.. are you saying that they have similar eigenvalues yet the eigenstates differ?
 
lucas_ said:
Hamiltonian operators on position and spin. I want to understand the quantum state of entangled system versus unentangled system. In entangled system, the quantum state doesn't just contain particle A or particle B but they are entangled.. yet when you measured them.. they are in particle A or B.. so how do they differ when end results in the same.. are you saying that they have similar eigenvalues yet the eigenstates differ?

No, I'm not saying anything besides that your question is (still) not well formed. What Hamiltonian exactly? Your confusion seems to be much deeper than you believe, as you seem to not understand how these things relate at all.
 
Jazzdude said:
No, I'm not saying anything besides that your question is (still) not well formed. What Hamiltonian exactly? Your confusion seems to be much deeper than you believe, as you seem to not understand how these things relate at all.

In entangled system of particle A and particle B, the quantum state doesn't contain just particle A and particle B but their combination.
In the case of a photon or electron in a double slit experiment, the photon quantum state contain path A or B.. so they are not entangled.
In quantum mechanics.. how are analysis of entangled and unentangled system differ? what subtopics do they fall under. They seem to have similar projection or eigenvalues.
 
Again, what is your Hamiltonian? If you ask for eigenvalues and eigenstates of the Hamiltonian, you have to specify it.
 
Jazzdude said:
Again, what is your Hamiltonian? If you ask for eigenvalues and eigenstates of the Hamiltonian, you have to specify it.

oh sorry not the Hamiltonian, but the position operator. In the entangled pair, how is its position operation differ to that of an unentangled pair? In the entangled pair, particle A and particle B are mixed.. so when performing the position operator, how come you still get the position of particle A and not their combined state?

btw.. what is the operator for spin?
 
The position operator only acts on a single particle state space. Its eigenstates are therefore the same as in the single particle case.
 
Jazzdude said:
The position operator only acts on a single particle state space. Its eigenstates are therefore the same as in the single particle case.

Thanks. What other operators only act on a single particle state space beside the position operator?
 

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