Talk:Exchange interaction

message: Aren't the "exchange interaction" and "exchange force" in the first paragraph two different things?  The first results from the antisymmetry of identical fermions without reference to interactions with other particles.  The second results from the exchange of bosons, whether the fermions are identical or not.  Maybe the "exchange force" should be discussed elsewhere.  —JerryFriedman 19:18, 15 February 2007 (UTC)
replies: text: I am not an expert on this subject, but I think that the example of a gluon (boson) passing between two quarks is inappropriate for this article. The "exchange" being discussed here is two fermions of the same type trading places with each other. When two atoms are close enough that an electron orbital of one overlaps an electron orbital of the other, the two electrons (of the same spin) can trade places in the overlap and this creates a repulsive force also known as the Pauli force. JRSpriggs 05:56, 16 February 2007 (UTC)
replies: text: Presently, exchange force is a redirect into exchange interaction, hence there my be a certain amount of overlap of differing material in the article. I will move some of the material into exchange force as its own article, although technically they may be the same thing in some discussions. --Sadi Carnot 16:19, 24 April 2007 (UTC)
thread_title: What is being exchanged?

message: The article gives one the impression that the exchange interaction only is a factor for electrons (or perhaps for fermions) -- it happens for both bosons and fermions, and I'd remove all reference to electrons since it happens for all fermions, not just electrons.
There is an excellent description of this in Griffifths, "Introduction to Quantum Mechanics", second edition, pages 207-210. Basically, identical fermions with overlapping wave functions are observed "further apart" than distinguishable particles, and identical bosons with overlapping wave functions are observed "closer together", where we think of distance here as the expectation value of the square of the difference of the positions of the particles.
Anyway, I think the subject is confusing enough already without making it look like a fermion only phenomenon etc. --Pmetzger (talk) 19:42, 28 January 2008 (UTC)
replies: text: I'll agree with P. Metzger too, an would like the plurality to return into the title as stated above, e.g.: Exchange "interactions" as well. It will possibly involve some redirectional consequences, but wouldn't so be better spoken of many interactions instead of much interaction? D.A. Borgdorff: 86.83.155.44 (talk) 00:49, 30 January 2008 (UTC)
replies: text: I'm not sure why it should be plural -- it is a unitary phenomenon, not several phenomena. --Pmetzger (talk) 02:32, 30 January 2008 (UTC)
thread_title:  Exchange interactions are not just for electrons/fermions 

message: The article says:
"For example, the exchange interaction results in identical particles with spatially symmetric wave functions (bosons) appearing "closer together" than would be expected of distinguishable particles, and in identical particles with spatially antisymmetric wave functions (fermions) appearing "farther apart".
Aren't fermion wave functions supposed to be totally antisymmetric (space/orbital symmetry X spin symmetry), and vice versa for bosons? Perhaps the article is correct if you consider the spatial wave function to be a complete wf in Hilbert space, but in that case the wording should perhaps be chosen more carefully.  —Preceding unsigned comment added by 93.141.69.128 (talk) 00:11, 23 June 2010 (UTC)
thread_title:  Incorrect wording on wave function symmetries? 

message: The article's equation (3) adds quantities C, B, and Jex to an energy quantity E0. The integrals C, B, and Jex contain only component wavefunctions phi (nondimensional) and distances, giving them units of some power of distance. Energy seems like it should have a different dimension, unless it is being nondimensionalized somehow.
And on the unperturbed hamiltonian definition: It contains two Coulomb attraction terms 1/r1 and 1/r2 - these should be from each electron to each nuclei, not from the electrons to the origin, right? (Could be more clear)
User:Anonymous  — Preceding unsigned comment added by 50.160.151.149 (talk) 02:54, 12 September 2014 (UTC)
thread_title:  Question on equations 4,5, and 6? 

message: In the text is mentioned "electron–proton attraction (ra1/a2/b1/b2)" but there is no such r_{a2} or r_{b1} in the equations. See in particular the expression of \mathcal{H}^{(1)} between equations (2) and (3). Since it is expected that the proton a electrostatically interacts with the electron 2, as well as the proton b with the electron 1, I also expect - \frac {e^2}{r_{a2}} and - \frac {e^2}{r_{b1}} terms.
Besides this, in the expression of \mathcal{H}^{(0)}, we have two more terms - \frac {e^2}{r_{1}} and - \frac {e^2}{r_{2}} that I don't understand. Are they the 2 missing terms I mentioned?
Anyway, something must be wrong, at least in the wording, if not in the content. The reference to ra1/a2/b1/b2 is a broken link, as far as r_{a2} or r_{b1} are concerned.
Check http://phycomp.technion.ac.il/~riki/H2_molecule.html for an equation that includes all these terms without issue with the wording. JPB (talk) 12:11, 6 August 2015 (UTC)
thread_title:  Missing Ra2 and Rb1 in the equations 

message: I think that this article is of very low quality. First, the Hamiltonian given for what is inconsistently referred to as hydrogen or helium has terms with no explanation, taken from a technical document. Then perturbation theory happens. Then the introduction of spins refers to a matrix in perturbation theory!
Griffiths quantum 5.1.2 finds expressions of the mean square distance between two particles with given wave functions for indistinguishable and distinguishable particles. For fermions and bosons this is \pm |<x>_{ab}|^2 (just \pm some positive term). Thus whenever there are Coulomb-like repulsive interactions, spatially symmetric particles will have a larger interaction energy for given wave functions. Then consulting this source, http://uw.physics.wisc.edu/~himpsel/449exch.pdf, we can establish that electrons of opposite spins are symmetric with respect to exchange of spatial parts of the wave function. There are no big Hamiltonians or perturbative things involved in this explanation. FrozenWinters (talk) 05:31, 26 December 2016 (UTC)
thread_title:  Proposed article re-organization