
#1
Jan1408, 10:55 PM

P: 555

Hi all
In Paul Tipler's book on modern physics (with Ralph LLewelyn) I read an explanation for the formation and stability of a molecule, which is based on Pauli's exclusion principle. This principle was responsible for a term in the energy equation, which yields also (naturally) a term in the force equation. Is this quantum force an independent interaction or is it possible to decompose this exchange interaction in terms of gravitational, eletromagnetic, weak and strong nuclear force? Best wishes DaTario 



#2
Jan1508, 01:30 AM

HW Helper
P: 1,273

The "exchange interaction" is due to requirement that the manybody wavefunction of a system of electrons be total antisymmetric with respect to particle interchange. In terms of singleparticle wavefunction this means that the electron "fill up" single particle states and no more than one eloectron can be in the same state. People do not usually consider exchange to be another type of force since it is just due to the symmetry of the wavefunction. And no it can't be decomposed into gravitation, electromagnetic, etc.




#3
Jan1508, 03:54 AM

P: 555

If it cannot be thought of as combination of the four fundamental interactions, and if it is responsible (at least in part) to something important and relevant as the stability of molecules, I see no choice other than consider exchange interaction as one of the fundamentals.
Best wishes DaTario 



#4
Jan1508, 11:14 AM

P: 869

Four or Five fundamental forces
Perhaps it is not considered a fundamental force because it acts instantaneously across the entire system (i.e. it has an infinite speed) and because iif there were an associated boson mediating the force it would have to have inifnite energy.
Otherwise I too wonder why it wouldn't be considered a force... 



#5
Jan1508, 12:59 PM

P: 18





#6
Jan1608, 07:23 AM

P: 555

There seems to exist, therefore, a force term (which in the case of K Cl is of the form A/r^{10} according to a solved exercise) implied by quantum mechanics. It still seems plausible to ask if this force can or cannot be derived from any one of the four fundamental interactions. Learning from Casimir effect, we may think of this force as eletromagnetic, in nature, but originated from quantum fluctuations (the r{10} dependence reminds me the casimir term) But no clue on how to estabilish this result. Best wishes DaTario P.S. in no place we can read in the book that coulomb repulsion between protons take part in this process. 



#7
Jan1608, 09:23 AM

P: 18

The force is electromagnetic In fact it's the coulomb force. Many people thinks ferromagnetism is due to magnetic force. It's impossible once magnetic force can do no work and ferromagnetism can do work. In fact ferromagnetism is due to the coulomb force in the exchange energy term.




#8
Jan1708, 12:43 PM

Sci Advisor
P: 779

I think danime has it right: if you set the charge of the particle to zero, then there is no force, exchange or otherwise! So there you go. The force is EM.
What about the centrifugal barrier in ordinary mechanics? You know there is a term in the effective potential that goes like L^2/(2mr^2) in three dimensions, and a similar term appears in the quantum Hamiltonian. What "fundamental" force do you associate with this term? It comes from the "centrifugal force" but we would never consider such a force "fundamental"  as a matter of fact, some people would claim that it isn't even a FORCE in the rigorous sense. It is strictly a consequence of the noninertial nature of the reference frame. I think you can make an analogy here. The "exchange FORCE" is not a "force" in the rigorous sense, but is a consequence of the quantummechanical nature of matter's electromagnetic interactions, in the same way that the centrifugal "force" is a consequence of the reference frame. 



#9
Jan1708, 12:51 PM

P: 18

Descartes said "In trascendental matters be transcendentally clear".
There's no such thing as exchange force. There's a term in the hamiltonian due to the electromangnetic interaction that lowers the total energy when identical particles are in such state, which depends on the hamiltonian in question. 



#10
Jan1708, 12:59 PM

P: 18

As an example we can cite the ferromagnetism.
Once the electrons are fermions their total wavefunction must be antisymmetric. When you construct the hamiltonian for say more than one electron interacting through coulomb force there are negative cross terms. If the terms are non null the total energy will be less so the nature prefers to make this terms non null. But the only way this terms can be non null is if the spins are parallel, once antiparallel spin wave functions are orthogonal. This creates an effect contrary to the coulomb repulsion once the more the wavefunctions overlap in the space the more effective is the exchange term. It's a brief description of the ferromagnetic effect. There other things as domains, anisotropies, etc... But that have nothing to do with what we are dealling. 



#11
Jan1808, 03:00 AM

P: 555

Besides, it seems that you both agree that exchange force is the electrical force plus quantum fluctuation effects. Note that you don't mention the quantum mystery of the magic numbers 2, 8, 18, that represent the electronic capacity of each quantum level in the atomic structure. The exclusion principle as I know it, is an "ad hoc" term in quantum theory. It does not appear as consequence of the Shroedinger equation (correct me if I am wrong...). Hoping we can see some light on this subject, DaTario 



#12
Jan1808, 04:31 AM

P: 18





#13
Jan1808, 04:34 AM

P: 18





#14
Jan1808, 10:45 AM

P: 869

Again, the only substantive difference I see between the quantum exchange interaction and the four fundamental forces is that the former is nonlocal. 



#15
Jan1808, 11:36 AM

P: 18





#16
Jan1808, 11:53 AM

P: 869





#17
Jan1808, 03:45 PM

P: 18

Do you want to have some guiding in studying quantum mechanics? 



#18
Jan1808, 03:48 PM

P: 18

Finally the topic was "Four or Five fundamental forces". By now four because even if you consider the exchange force as a real force It's not fundamental because it requires the electromagnetic interaction which is fundamental itself.



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