Talk:Pauli exclusion principle

message: Need a little more clarification for laymen: there's a bound for the amount of information in a finite region of space (Bekenstein bound, which depends on the amount of energy-mass in that region. Does it mean if there's an infinite amount of energy in a region of space then there's an infinite amount of information? Should there be an upper bound for energy-mass if Pauli exclusion principle really holds true? Also, if that's the case then singularity is ruled out?Mastertek (talk) 14:49, 23 October 2011 (UTC)
thread_title: Energy-mass limit in given finite space

message: Conceptually, it is simple to understand the correspondence between fermions/matter and bosons/[fields; energy; ??]. It's an important point for this article too, I think - it's one of the most important consequences of the Pauli principle. What's the best way to describe it?
On one hand, describing bosons as "fields" is a little misleading, because fermions are also described as fields in QFT. The reason light is classically thought of as a "field" instead of a particle has as much to do with the fact that the photon is massless (hence long-range, hence classically detectable as a field) as the fact that it is a boson. So the distinction isn't too clear.
On the other hand, describing bosons as "energy" is also misleading, because obviously fermions carry energy just as well as bosons.
Thoughts? CYD
:Both fermions and bosons can be considered as waves or fields. Even atoms can be bosons such as sodium and they behave accordingly at low temperatures. The most intuitive distinction I can think of is between matter and non-matter particles. But as for sodium even this distinction becomes blurry at low temperatures, so be careful. --Thorseth (talk) 10:21, 26 May 2010 (UTC)
thread_title:  Correspondence 

message: There's a hint in Quantum Physics by S. Gasiorowicz that fermions do not require a totally antisymmetric wavefunction if there is sufficient separation. From memory, it said something like: "the reader might expect that if we have one electron on earth and one on the moon, they won't require antisymmetrization... Indeed, even at lattice spacing distances of 5-6 angstroms, antisymmetrization is usually unnecessary".
Unfortunately, the only mathematics presented to support this was a calculation of the amount of overlap in probability densities between distant electrons.
That's as much as I know - I couldn't write an authoritative summary on the matter. If true, it would impact on not only this article, but also identical particles and fermions, and perhaps others.
-- Tim Starling 11 Oct. 2002
I believe he's saying that, under certain circumstances, you can make an approximation of ignoring antisymmetrization. -- CYD
:I've posted a more detailed response over in the identical particles discussion page.  But the gist is this: The two-particle wavefunction (for fermions) is always antisymmetric, but if the two particles are far apart (i.e., if the single-particle wave functions don't overlap significantly) then one of the two terms in the antisymmetric wavefunction will be very small, and you'll be left with a two-particle wavefunction that's approximately equal to what you would have had if you didn't bother to make it antisymmetric.  Hence, when it comes to actually calculating anything, the antisymmetrization is unnecessary, very unnecessary. -- Tim314 16:11, 2 May 2007 (UTC)
thread_title:  Antisymmetric 

message: Is the Pauli exclusion principle a complicated way of saying that two things can't be in the same place at the same time?
Answer: this is one consequence of the Pauli exclusion principle. See new section Stability of Matter.  Dirac66 (talk) 02:41, 7 May 2008 (UTC)
thread_title:  Simplification 

message: Pauli exclusion principle seems to be an ADDITIONAL assumption to the
quantummechanical principles, since it seems (to me) that there is no
proof WHY spin-half particles have anti-symmetric wavefunction 
and integer spin are symmetric.
If this is indeed true, can someone edit the text in this respect?
The exclusion principle is explained a thousand times on the web,
but (almost) no one mentions this aspect. -- John
One of the results of quantum mechanics is that spin is quantized - the spin of a particle is either an integer or a half-integer times hbar. There is a theorem in relativistic quantum mechanics, called the spin-statistics theorem, which says that particles with integer spin obey Bose-Einstein statistics, whereas particles with half-integer spin ovey Fermi-Dirac statistics, and therefore obey the Pauli exclusion principle. In non-relativistic quantum mechanics, however, the Pauli principle must be postulated (and there is certainly enough experimental evidence to call it an empirical fact.) See identical particles for a little discussion of this. -- CYD
for CYD:
do you mean the exclusion principle holds only at short distances? because i just dont fully understand it, if no two 1/2 spin particles can occupy the same quantum state every atom of the same element will be different, and (i dunno much, just a guess) worse since the energy levels are quantized we wont have that many hydrogen atoms in the universe, but we do.
also, forgot to add, (remember i'm only a beginner at this stuff, so dont laugh at my questions), when the electrons in a lithum are not observed, so they remain in "waves", their spin is in superposition, so how can the exclusion principle apply to them??? i mean, doesnt it only work when you have an eigenvalue of the obserable? i know atomes will collapse that way but can you tell me why it doesnt?
thanks
-protecter
A note to questions posed above: Each of those millions and billions of Hydrogen atoms or electrons in various Lithium atoms are in different quantum states. An electron in its ground state in one Hydrogen atom is in an entirely different quantum state (i.e. posesses a different Hamiltonian or energy state) than another electron in a different Hydrogen atom some distance away. In fact, if you were to push two Hydrogen atoms close together, the Pauli exclusion principle predicts that there will arise some pressure between the two as the sates begin to overlap, in order to resist that overlap, and indeed, this pressure is detectable experimentally. The Pep holds - no two fermions can exist in the same state.
--zipz0p
: I am puzzled by this point as well. You (zipz0p) state that two ground-state electrons in two different H atoms are in a different quantum state. But: the article states that for electrons, PEP is equivalent to saying the four quantum numbers cannot all be the same. Which of the four quantum numbers is always different for two ground state electrons in different H atoms? It seems to me (non-physicist) that some implied qualification is being left out. Clarification would be much appreciated! Mrhsj 01:56, 19 January 2007 (UTC)
replies: text: The answer to that question is that you need an additional label for which atom the electron is in.  In a many-atom situation, the PEP holds for the four quantum numbers plus atom label taken together.  The statement in the article about the four quantum numbers only holds for a single atom.  Another way of thinking about the atom label I talk about above is to introduce a continuous position variable that marks the center of mass of the atom the electron is in.  In summary, the PEP holds for the complete set of quantum or classical coordinates required to uniquely identify a particle.  I hope this helps. -- Custos0 01:19, 2 March 2007 (UTC)
replies: text:  Yes - that's what I was looking for. Thanks! Mrhsj 05:08, 2 March 2007 (UTC)
thread_title:  Assumption 

message: I think since the Exclusion Principle is a recognised title, then this article should reside under Pauli Exclusion Principle, rather than Pauli exclusion principle. I have been reading many published texts recently on the subject and all seem to use the capitalised version. What does everyone think? - Drrngrvy 16:26, 6 January 2006 (UTC)
thread_title:  Pep vs. PEP 

message: I think the article should perhaps say something about the fact that the PEP is the primary reason that material objects collide macroscopically and that we can stand on the ground, etc. It is commonly held that this is due to electromagnetic forces, but in fact, the dominant force is a product of the PEP: electrons in the atoms of the separate surfaces will effectively repel one another as the surfaces approach and the electrons come closer to occupying the same state (which is forbidden by the Pep).
--zipz0p
:What is the force that's responsible for maintaining the PEP? As a layperson, I'm having trouble finding an explanation of the PEP. Mathematical descriptions and predictions are fairly easy to find, but are not readily accessible to non-physicists. Why can't two identical fermions occupy the same space? The second para of the overview talks about wave functions - these are like descriptions of the probability of a particle occupying a quantum space, is that correct? I apologise for my lack of understanding, but i hope we can use that to further improve this article. Ethidium 18:15, 11 May 2007 (UTC)
thread_title:  Other effects of the Pep 

message: How about discussing "matter occupies space exclusively for itself and does not allow other material objects to pass through it" in terms of Fermi pressure keeping matter apart?  It might be useful to point out how much denser a Neutron Star is, where gravity overcomes to Fermi pressure of the electrons to give a star of the density of an atom's nucleus. Custos0 01:28, 2 March 2007 (UTC)
thread_title: Fermi pressure?

message: Thanks to those who added to the Consequences section to discuss the solidity of matter. I agree with Custos0, that further examples of neutron stars could be a good example, possibly worthy of a separate section from the Consequences section.
I edited the last paragraph of the Consequences section to reflect that it is impossible to determine the state of matter inside a black hole, as this is beyond the event horizon, and no information about the inside can be passed out. However, after posting it, I thought some more about it, and am not sure that it is appropriate to even mention this discrepancy here. Is it perhaps not important enough to the subject, or not within the scope of the article?
Also, I wonder if the PEP is actually violated if the particles themselves have no physical extent. Can they actually occupy the same spatial coordinates, then? It seemed to me that they mathematically could, but that this would be a violation of the PEP, hence what I wrote in the article. Please correct me if I am mistaken, or elaborate if the understanding is not deep enough. zipz0p 00:41, 11 August 2007 (UTC)
thread_title: Consequences

message: The bits "The Pauli exclusion principle mathematically follows from applying the rotation operator to two identical particles with half-integer spin." and "The Pauli exclusion principle follows mathematically from the definition of the angular momentum operator (rotation operator) in quantum mechanics" seem to imply that the PEP is not a principle, but a consequence of quantum mechanics. This is not correct, as can be seen for example in "No spin-statistics connection in nonrelativistic quantum mechanics" by  llen, R. E.; Mondragon, A. R., eprint arXiv:quant-ph/0304088. The PEP is a postulate and cannot be derived in quantum mechanics; it is a consequence of the spin-statistic connection in quantum field theory. You can have bosonic one-half spin particles in quantum mechanics without any contradictions arising. The statement "The Pauli exclusion principle can be derived starting from the assumption that a system of particles occupy antisymmetric quantum states." is trivial, because the Pauli exclusion principle can be formulated as saying that fermions occupy antisymmetric quantum states.  —Preceding unsigned comment added by 148.214.16.76 (talk) 22:02, 21 November 2007 (UTC)
replies: text: I removed all the misstatements. There is a relativistic derivation along these lines, but it requires rotating the particles in time, not just in space, so that the order of the operators in the path integral is interchanged.Likebox (talk) 23:53, 15 May 2008 (UTC)
thread_title: Incorrect statements

message: The article on Freeman Dyson states that he proved that the PEP was the true cause of the Normal
Force (eg. the force of a brick on a table).  If this is true, this is remarkable and news to me, and should
be mentioned here.  But I have not looked into the articles on the Dyson article, but if they check out, 
this should be included in the article on PEP Substar (talk) 04:15, 24 April 2008 (UTC)
thread_title: PEP Causes the Normal Force?

message: Suggestion: I'm not qualified to write this up, but doesn't the imaging of the pentacene molecule deserve some mention here, since, as I understand it, it depends on the PEP. See http://www.newscientist.com/article/dn17699-microscopes-zoom-in-on-molecules-at-last.html and http://www.sciencemag.org/cgi/content/abstract/325/5944/1110  —Preceding unsigned comment added by 80.176.244.187 (talk) 10:58, 28 August 2009 (UTC)
thread_title: Imaging of Pentacene Molecule

message: Peter Lynds has been promoting the idea of a cyclic universe where singularities are not allowed.  He never explains why.  And he may be wrong as far as black holes inside the Universe.  Is it possible that PEP comes into play if a black hole becomes too big?  By this, I mean would gravity ever become so powerful that it would try and force particles to occupy the same space - the resulting interaction would cause a bounce effect where the Exclusion Principle would force the black hole to explode.  As to Lynd and his cyclic universe theory a universe size big crunch may offer this type of showdown between gravity and particles occupying the same space.  Comments?  --Dane Sorensen (talk) 13:39, 27 November 2009 (UTC)
thread_title: The Big Bounce

message: The results of the Bethe ansatz do not map to a free Fermi gas unless the delta functions repulsion of the one-dimensional bosons are infinitely strong. The bose-fermi map in the case of finite delta-repulsion does not provide a solution in this case, since both theories are interacting. The Bethe Ansatz article can include the nonlinear schrodinger equation as an example, of course, but this article is somewhat more elementary.Likebox (talk) 23:37, 2 December 2009 (UTC)
thread_title:  Finite vs. infinite repulsion 

message: This article is extremely technical. I cannot make sense of it :(
67.204.204.104 (talk) 07:19, 17 January 2010 (UTC)
thread_title:  Technical 

message: What about molecules that violate the Pauli principal?
Citation: http://iopscience.iop.org/1742-6596/67/1/012033  —Preceding unsigned comment added by 24.42.255.117 (talk) 01:29, 22 March 2011 (UTC)
replies: text: I have moved this new section to the end. The paper you cite does not report evidence that the Pauli principle is violated. It reports a search for such evidence, in an experiment which was more sensitive than previous searches. According to the abstract, the parameter 1/2β2, which is a measure of any possible violation, has an [upper] limit of 4.5 × 10−28. There is no lower limit, which means that the result is consistent with zero. We can therefore continue to consider that there is no violation of the Pauli principle, unless and until some future experiment proves a result different from zero. Dirac66 (talk) 13:44, 22 March 2011 (UTC)
thread_title:  Violations 

message: Is the Pauli principle itself a fundamental property of matter (as far as we know), or is it caused by some other more fundamental property (or properties)? Please add. -- 77.189.26.217 (talk) 19:27, 12 November 2011 (UTC)
replies: text: I think the article is already about as clear as it can be on this: the Pauli exclusion principle is equivalent to (or a direct result of) the antisymmetry of a fermion's quantum-mechanical wavefunction.  There's not much room for something more fundamental than that within the current framework of quantum theory.  Quondumtalkcontr 13:11, 16 November 2011 (UTC)
thread_title:  Fundamental property of matter? 

message: There should be a place on the internet where the abstract reasoning of the Pauli Exclusion Principle should be explained, unfortunately this is not the place.
There are two conceptual aspects that this page should be designed around, first the history, why [for instance] the need to define electron probability distributions (i.e. orbitals) that drove its discovery. However the second and more important principle separate behavior of particles with half spins from particles with integer spins (bosons).
The underlying abstract principle is that Pauli-exclusion statistics applies to particles with half spins (e.g. the statistcal size of an electron, proton or neutron is considerable smaller than the composites they form (Atoms and atomic neucleus) because of repulsion required to maintain symmetry statistics.
But the math used to explain symmetry statistics in this article is awful, and this comes from someone who has written several science articles involving advanced statistical techniques. If I don't follow your argument past the first sentence, you cannot expect lay readers to follow it either,
The rule here is if the individual needs to spend more than a few seconds to figure out the meaning of a modest size sentence, they have already left the page
"
The Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to requiring the wavefunction to be antisymmetric.
"
How do you define symmetry? Is it defined by spatial postioning, spin, momentum? What precisely do you mean by antisymmetrical? There are a dozen different ways to break symmetry, there is mirror symmetry, axial symmetry, radial symmetry, spherical symmetry,rotational symetry (such as the highest orbitals of the benzene ring), thus there are 100s of ways to be antisymetrical.
"
An antisymmetric two-particle state is represented as a sum of states in which one particle is in state \scriptstyle |x \rangle and the other in state \scriptstyle |y\rangle:
:
|\psi\rangle = \sum_{x,y} A(x,y) |x,y\rangle
"
And this does not make sense, what is |x,y\rangle, is this the combined wave function statistic for the two. What does A(x,y) stand for, and what quality is being summed of x, and y?
So immediately you have lost 99.9% of the readers, and the explanation only gets worse as one moves to the next equation, the reader, bored to tears, has already clicked on something to see if they could link to Adolf Hitler in 3 more links.
I think the key point is that symmetry is maintained in a spatial proximity in some existing (albeit mobile) frame, the quantum state is defined in space/time (as faulty as this mode of definition is prone to be in a heisenberg context). True spatial symmetry does not exist at the atomic size level, that needs to be defined, but statistical symmetry, the tendency for particles to coexist in a very rough, statistically definable. What was attempted above and failed, was to define that statistical symmetry. Heisenberg noted that it is impossible to define a simulataneous position/momentum, and therefore even within orbitals such spatial symmetry does not exist outside of a range. In other words, the range parameter has a meaning that is not explained, as a consequence the user will not be able to follow this.
The classical question would be why do not electrons simply lay on the atomic nucleus, since negatively charged particles are attracted to the positively charged nucleus. Even when helium is condensed at absolute zero, its atoms maintain distance between electrons in the various orbitals, thus even though the symmetry is not true perfect symmetry, the need to maintain it is sufficient at the lowest energy state for certain stable particles. Thus the need to maintain symmetry is an observation of nature. 
The second key question is why does symmetry need to be maintained and how does this pertain with particles with 1/2 spins. The answer is that electrons within the atom are driven to maintain a certain level of angular momentum (rotational energy) to statistically maintain distance from one another but also from the nucleus.
The diamond I think is a perfect example for defining this type of issue, while diamond is the hardest and therefore stiffest molecule known to mankind (excluding the surfaces of dense boson such as neutron stars), both the electrons, their orbitals and the atoms within the nuclei are wobbling in space, but they are confined because of the need to maintain symmetry there is some stasis in the sp3 orbitals of the diamond molecule, where as super cooled helium (an effective boson) exhibits super fluidity. But it is the key need to maintain spherical symmetry in the sp3 orbital and polar 'spin' symmetry of electrons in those 'orbitals' that defines the strength of the diamond C-C bond. Thus symmetry is observed preference in arrangement of electrons as a key observation, placing particles with identical half 'spin'  in the same quantum 'aspect' causes symmetry to cancel, resulting in instability (I think in this case, diamond electrons would fly into space the atoms would follow negative charge and you would have very few long lasting stable molecules in the Universe). Since stability is the observation then symmetry can be explained by the need for symmetry quantum states of half 'spin'. The math needs to explain this,
Why do particles with half-polar/'spin' states apply subtraction in defining the statistic whereas bosons (with integer) spins undergo addition? This is the statistical question, that needs to be defined. What, statistically, does up and down correspond to in electrons? How does one define this, and better yet how is this explained?
Within that context fermions exist in symmetrical quantum states, the lowest level of which is spin/dipole pairing of electrons, such as those that make diamond and exceptionally resilient structure. So that the spatial and momentum features of the quantum state have particular symmetry aspects. If you are generically referring to those symmetry aspects, then define that.
PB666 yap 18:58, 27 December 2011 (UTC)
thread_title: How to make this page useful

message: Just a note to reassure editor 31.18.248.254 whose edit summary indicated uncertainty. Yes, the rule is one electron per state. And I agree that the sentence you modified is clearer with your addition of the word electron. This word does now appear three times in the sentence, but I think that in this case the repetition is helpful. Dirac66 (talk) 00:50, 14 October 2012 (UTC)
thread_title:  Yes, one electron per state. 

message: The Pauli exclusion principle applies to all electrons as they are indistinguishable. I refer to the wikipedia article on identical particles.
:"Even if the particles have equivalent physical properties, there remains a second method for distinguishing between particles, which is to track the trajectory of each particle. As long as we can measure the position of each particle with infinite precision (even when the particles collide), there would be no ambiguity about which particle is which. The problem with this approach is that it contradicts the principles of quantum mechanics. According to quantum theory, the particles do not possess definite positions during the periods between measurements. Instead, they are governed by wavefunctions that give the probability of finding a particle at each position. As time passes, the wavefunctions tend to spread out and overlap. Once this happens, it becomes impossible to determine, in a subsequent measurement, which of the particle positions correspond to those measured earlier. The particles are then said to be indistinguishable."
And this source http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double%20Well.html
Wolfmankurd (talk) 21:06, 24 November 2013 (UTC)
replies: text: The example is given for an atom. If there are two separate atoms, nothing prevents an electron in one atom to be in the same state (i.e. posses the same quantum numbers) as the electron in another atom. Headbomb {talk / contribs / physics / books} 21:17, 24 November 2013 (UTC)
replies: text: Headbomb is correct. But I will add an example just to make the point clearer for Wolfmankurd. Consider a system of ten helium atoms in some volume. If the first He atom has its two electrons in its 1s orbital, do you really think the second He atom must have its two electrons in its 2s orbital, and the third He atom must have its two electrons in its 2p subshell, and so on?? In the real ground state of the system, each He atom has two electrons in its own 1s orbital. Dirac66 (talk) 21:30, 24 November 2013 (UTC)
replies: text: The argument made in the link I gave is that they would be in the ground state but the associated energy levels would be different. I understand chemists often use orbital and energy interchangeably but that's not the case. The difference it's calculated and shown to be minuscule calculated particle in a box style( or well two particles in two boxes). Another argument made is that while we consider electrons localised to different atoms to be distinguishable in reality they are indistinguishable especially after a while when the wave functions will spread and overlap. Since the Pauli exclusion principle states that no two identical fermions can occupy the same quantum state. And electrons are identical they must all have at least subtle different energy levels. Wolfmankurd (talk) 21:48, 24 November 2013 (UTC)
replies: text: I think that the article is not clear enough on this. Wolfmankurd is obviously correct in saying that as electrons are identical, no two electrons can occupy the same state, and I think that the wording of the example should not leave something like this unclear. An electron in the 1s orbital of atom A is not in the same state as the 1s orbital of atom B: location comes into the definition of a state. The wording should ideally reflect this dependence of the state on position.  The problem is that the "four quantum numbers" are not sufficient to specify the state; a further "quantum number" (giving which atom) must be given.  I had intended this to be implicit in my wording, but it is still not clear.  This is complicated by that the eigenstates of a separated pair of identical atoms are not the eigenstates of single atoms.  Could we look for a wording that makes it more obvious to the reader that in the example, where the electron is contributes to its state? Our objective here is to explain to the reader, not only to the OP. Should we start the example with "For example, in an isolated atom..."? —Quondum 00:35, 25 November 2013 (UTC)
replies: text: Perhaps it would be best to use these words instead of "for a given atom", since it is really for an isolated atom that the state of an electron is specified by four quantum numbers. For an ensemble of atoms, the correct description would be given by band theory in which orbitals on different atoms overlap slightly and form an energy band. However for a gas at low pressure, the overlap and the bandwidth are negligible. And all this is too complicated for the introduction of this article. Dirac66 (talk) 01:00, 25 November 2013 (UTC)
replies: text: I've made the change; the wording sort of sidesteps the problem of interpreting contexts with more electrons, but seems correct to me.  It is probably worthwhile keeping the example in the lead simple at the expense of not giving much insight into when more electrons are to be considered.  If this can still be misinterpreted, feel free to comment.  —Quondum 18:51, 25 November 2013 (UTC)
thread_title:  In an atom, or all electrons? 

message: The article should reflect this. V8rik (talk) 18:54, 16 June 2014 (UTC)
replies: text: Well, he started in 1925 with electrons of course. Do you know when it was first proposed that the exclusion principle refers to all particles of half-integral spin? That information should be in the article. Dirac66 (talk) 01:32, 17 June 2014 (UTC)
replies: text:  more info is missing , the original citation for instance: http://dx.doi.org/10.1007/BF02980631. Did some googling but I was unable to find out who coined the phrase fermion and when. Possibly Dirac. V8rik (talk) 14:17, 29 June 2014 (UTC)
replies: text: Good work finding that source - I encourage you to include it in the article. And the word Elektronengruppen in the title confirms that he was thinking of only one type of particle. Perhaps we should just say that the extension to all fermions was "later", at least until someone finds the exact reference. Dirac66 (talk) 14:55, 29 June 2014 (UTC)
replies: text: Update: I have now corrected the intro to say that the principle was stated for electrons in 1925 and all fermions in 1940 with the spin-statistics theorem. I have also added the original 1925 citation given above by V8rik at the end of the History section. Finally the answer who coined fermion is in the Fermion article - it was indeed Dirac, in 1945. However I don't think this information is needed in this article. Dirac66 (talk) 01:30, 24 May 2016 (UTC)
thread_title:  Pauli did not discuss fermions in 1925 

message: :I am trying to understand how the  four fundamental forces (strong nuclear, electromagentic, weak nuclear, gravity) relate to covalent bonding. The webpage I look at points at the Pauli exclusion principle and the haze of chemistry. In chemistry you learn that there are s orbitals, p orbitals, yadda yadda. Isnt all this just saying that nuclear forces are anisotropic or not isometric while electrostatic and gravitational forces are isotropic or isometric? Mrdthree (talk) 08:10, 24 August 2014 (UTC)
thread_title: Pauli: Nuclear forces are anisotropic?

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thread_title:  External links modified 

message: Since nonrelativistically, particles can have any statistics and any spin, there is no way to prove a spin-statistics theorem in nonrelativistic quantum mechanics. 
Should this read "Since, nonrelativistically, particles can have any statistics and any spin, there is no way to prove a spin-statistics theorem in nonrelativistic quantum mechanics."?
Professor Bernard (talk) 19:41, 19 November 2021 (UTC)
replies: text: Um, where do you see this sentence in the article? Dirac66 (talk) 21:59, 19 November 2021 (UTC)
replies: text:  The sentence occurs further up on this talk page. Its punctuation has marginal relevance to improving the article. HouseOfChange (talk) 04:25, 20 November 2021 (UTC)
thread_title:  Missing Comma 

message: The introduction has a link to quantum system, which links to quantum mechanics, which doesn't say what a "quantum system" is.  Is there a better link to explain the term?  Bubba73 You talkin' to me? 23:14, 21 September 2023 (UTC)
replies: text: A quantum system is a system which obeys (the laws of) quantum mechanics. So I would suggest modifying the end of the first sentence to read "... cannot occupy the same quantum state simultaneously within a system which obeys the law of quantum mechanics." Dirac66 (talk) 01:37, 22 September 2023 (UTC)

text: Done. Dirac66 (talk) 14:27, 18 December 2023 (UTC)
thread_title:  Quantum system