- #1

edpmodel

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- TL;DR Summary
- Can four (or more) electrons form a completely antisymmetric joint spin wave function？

Can four (or more) electrons form a completely antisymmetric joint spin wave function？

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- Thread starter edpmodel
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- #1

edpmodel

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- TL;DR Summary
- Can four (or more) electrons form a completely antisymmetric joint spin wave function？

Can four (or more) electrons form a completely antisymmetric joint spin wave function？

- #2

Vanadium 50

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If I swap 1 and 2 and the sign flips, and 1 and 3 and the sign flips, what happens when I swap 2 and 3?

- #3

edpmodel

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If I swap 1 and 2 and the sign flips, and 1 and 3 and the sign flips, what happens when I swap 2 and 3?

In some textbooks and articles, joint spin wave function of three and four electrons are provided. But I have not seen the joint spin wave function of three or more electrons multiplied by their space wave function. I doubt it can't be done at all.

But multi-electronic systems do exist in reality. Something may be wrong with quantum theory.

- #4

DrClaude

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If your question is whether we can write a spin state for many electrons that is anti-symmetric with respect to the exchange any two electrons, then the answer is of course yes. The simplest procedure to construct them is a Slater determinant.In some textbooks and articles, joint spin wave function of three and four electrons are provided. But I have not seen the joint spin wave function of three or more electrons multiplied by their space wave function. I doubt it can't be done at all.

But multi-electronic systems do exist in reality. Something may be wrong with quantum theory.

By the way, the state doesn't have to be separable into spatial and spin parts for it follow the Pauli principle.

- #5

PeterDonis

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No, something is wrong with your understanding of how quantum states work.Something may be wrong with quantum theory.

Remarks like this are a good way to get yourself a warning.

- #6

Vanadium 50

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Something may be wrong with quantum theory.

Of course, it's never "There must be something I don't understand." It's always "there is a problem with conventional science."

- #7

edpmodel

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Sorry, I made some mis-expression. I should mean "completely antisymmetric joint spin wave function of 4 or more electrons".If your question is whether we can write a spin state for many electrons that is anti-symmetric with respect to the exchange any two electrons, then the answer is of course yes. The simplest procedure to construct them is a Slater determinant.

By the way, the state doesn't have to be separable into spatial and spin parts for it follow the Pauli principle.

- #8

edpmodel

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Sorry, I made some mis-expression. I should mean "completely antisymmetric joint spin wave function of 4 or more electrons". May I understand it that there is no completely antisymmetric joint spin wave function of 4 or more electrons.No, something is wrong with your understanding of how quantum states work.

Remarks like this are a good way to get yourself a warning.

- #9

DrClaude

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- #11

edpmodel

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I remarked "Something may be wrong with quantum theory". I meant our understanding of QM might have mistake. QM is correct, but our understanding of it is not always so.

- #12

weirdoguy

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but our understanding of it is not always so

Can you give an example?

- #13

edpmodel

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I agree. I am working on a model where a joint WF with anti-symmetric joint spin part is desired.

I seem to have obtained a wave function with mixed antisymmetry, which exactly meets my expectations, but it cannot meet the conservation of angular momentum. I should have an argument to support such a result.

- #14

PeterDonis

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My remarks in post #5 apply to this as well. You should not presume to make such claims about "our" understanding.I remarked "Something may be wrong with quantum theory". I meant our understanding of QM might have mistake. QM is correct, but our understanding of it is not always so.

- #15

PeterDonis

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Personal theories and personal speculations are off limits here.I am working on a model

- #16

PeterDonis

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This was answered in post #9.May I understand it that there is no completely antisymmetric joint spin wave function of 4 or more electrons.

- #17

PeterDonis

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