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What the heck is meant by Pauli force/effect ? 
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#1
Mar412, 08:56 AM

P: 1,412

I'm a last year physics undergrad and whenever I have a physics class given by an experimental physicist (e.g. solid state physics), they sometimes say things like "... and because of the Pauli force these two electrons are repelled ..." and whenever I enquire about what is meant, I get an answer like "it's due to the Pauli exclusion principle".
But the latter only states that two fermions cannot be in exactly the same state; it says nothing about a repulsive force that acts on two fermions close to each other. In essence the Pauli exclusion principle does nothing to prevent two fermions in being arbitrarily similar states, as long as the states are not exactly the same. So what is the deal: is there an actual Pauli force additional to the Pauli exclusion principle (NB: let's not get into a semantic discussion about the word "force", call it what you will, I'm simply referring to the socalled repulsive effect of two fermions close to each other)? Or are my experimental physicis professors botching the concept of Pauli exclusion principle, making their arguments using it fallacious (i.e. there is only the Pauli exclusion principle, no repulsive effect)? 


#2
Mar412, 09:46 AM

P: 97

I think it's common in solid state physic to do the same error, I've read the same thing in the Ashcroft and Mermin book to justify the LennardJones potential repulsive term. Pauli principle states that the state of a system of fermions is antisymmetric in the excange of two fermions. It can be interpret with a effective force when, for example, you use the HartreeFock approximation. In doing this you find that the antisymmetry of the wave function acts as an additiona term in the Hamiltonian, the "excange energy". This energy is though not necessarily positive, for example in the "jellium" model you find its effect is actractive. The specific form of this energy depends on both the interaction and the wavefunction you're using as an approximation. In conclusion it's right to think about the Pauli principle as an effective energy in some approximation, but you can't know a priori if it's an actractive or a repulsive contribution. Ilm 


#3
Mar412, 01:32 PM

P: 1,412

I see, interesting... Do you know of a source that addresses this issue, i.e. that mentions the common fallacious reformulations and in what ways it is correct (apparently related to the HartreeFock approximation)?



#4
Mar512, 04:33 AM

P: 97

What the heck is meant by Pauli force/effect ?
I don't know where to find a general treatment of this issue. You can simply try to find something on the excange energy and then constate it can be both positive or negative, maybe checking this explicitly in different examples. For a simple treatment of HartreeFock approximation you can read almost every solid state physic book (check it on physics forum), even Ashcroft, Mermin, Solid State Physics (I personally hated this book ). You can certainly find some example here where antisymmetry of the state produce a positive term in the energy of the system. Only believe in what is demonstrated though For a rigorous treatment (but not so easy) of HartreeFock approximation look for books on manybody quantum physics like Fetter, Walecka, Quantum Theory of ManyParticle Systems. Here you can find even the very simple example of the jellium model (not using HartreeFock if I remember it right), where antisymmetry of the state produce a negative term in the mean energy of the system. edit: to avoid misunderstanding, to my knowledge treating antisymmetry of fermions states as an effective potential is not strictly related to HartreeFock, which is only one of the possible approximations resulting in such a term in the Hamiltonian. Ilm 


#5
Mar512, 04:33 AM

P: 229

This question has in fact been asked a couple of times before on PF, for example by myself a year or two ago, see here:
http://www.physicsforums.com/showthread.php?t=409034 The discussion gets a bit offtopic after a while, but you should at least read through the first pages. It is clear from that discussion what the standard explanation for this issue is, but I'm not so sure that it explains it fully for me (yet, maybe it's only a matter of thinking it through/working through math). 


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