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edpmodel
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- 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？
Vanadium 50 said:I don't know what you mean, but probably no.
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?
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.edpmodel said: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.
No, something is wrong with your understanding of how quantum states work.edpmodel said:Something may be wrong with quantum theory.
edpmodel said:Something may be wrong with quantum theory.
Sorry, I made some mis-expression. I should mean "completely antisymmetric joint spin wave function of 4 or more electrons".DrClaude said: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.
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.PeterDonis said:No, something is wrong with your understanding of how quantum states work.
Remarks like this are a good way to get yourself a warning.
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.Vanadium 50 said:Despite the OPs protests that QM is fundamentally broken, we know from chemistry that what he wants just doesn't happen. Lithium is an alkali metal, not a halogen. Beryllium is a metal, not an inert gas. Helium is an inert gas, not a metal.
edpmodel said:but our understanding of it is not always so
I agree. I am working on a model where a joint WF with anti-symmetric joint spin part is desired.DrClaude said:I don't see how you could do it for even three electrons. As soon as you have more than two, two of them must have the same spin, hence it is impossible to form an anti-symmetric spin state. In any case, you need more degrees of freedom to satisfy the Pauli exclusion principle, so it all fits together: the full wave function will be anti-symmetric, but it is no longer separable into a spatial part and a spin part.
My remarks in post #5 apply to this as well. You should not presume to make such claims about "our" understanding. Your understanding of QM might not be correct.edpmodel said: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.
Personal theories and personal speculations are off limits here.edpmodel said:I am working on a model
This was answered in post #9.edpmodel said:May I understand it that there is no completely antisymmetric joint spin wave function of 4 or more electrons.