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Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: You didn't comment the other two questions, which I posted: "WHICH THEORIES IN HIS FIELD ARE AXIOMATIC", and "whether this is an axiomatic theory or not...". Does this mean that you agree with me that these are mathematical questions? As to the first one - “WHETHER THERE EXISTS A MATHEMATICAL MODEL describing this or that phenomenon” - I don't agree with you, because a mathematician who work in this field should know the applications of his activity. On the contrary, a physisist very likely will say that this is not physics, since the question is about mathematical models.
Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: An explanation to non-robots, why this is bad: this makes impossible the communication between specialists and non-specialists (because to ask a robot anything, you must be enough sophisticated in his specific language, so you must be a specialist), this leads to the lack of understanding between different groups of people in society, and, being a kind of rudeness ("hamstvo" in Russian), this contradicts to the ethic norms. Is that clear, or I should reformulate this in some special langauge?
Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: In addition to what I said: when I see a text with words like "postulate" or "axiom", I can ask a specialist, whether this is an axiomatic theory or not, and whether it describes the phenomena I am interested in. Dima, I think, I understand your idea: you think that a specialist must be a robot. Moreover a badly adjusted robot, who can't understand normal language which people use for communication. Such a robot that for asking him something you should write a special program, like in FORTRAN, otherwise he will be answering only: "this is not my field, rewrite your question!".
Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: 1) I already asked Jacques, now it's his turn. 2) That's the main point: "you must always specify the mathematical model... otherwise it is not a mathematical question". I don't agree. I can ask WHETHER THERE EXISTS A MATHEMATICAL MODEL, describing this or that phenomena, and this also will be a mathematical question for the mathematicians working in close fields (especially in fields with the same name, like "quantum mechanics"). I can also ask a mathematician WHICH THEORIES IN HIS FIELD ARE AXIOMATIC SYSTEMS, and this also will be a mathematical question. Should I explain, why?
Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: 3) You compel me all the way to specify not only WHAT I would like to be proved, but also HOW I expect this to be proved. Initially you told that I should mention the Schrödinger operator, now you speak about the Berezin-Shubin model. Why is it so important? If you know what should be proved (example: the statement on the structure of orbits), why the question remains unclear until I explain how I think this must be proved (solving Schrödinger equation, or using the Berezin-Shubin model)? I used to think that the question HOW is extra in the formulation of problem.
Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: 2) I already explained what I mean by "proof". If you ask what exactly I would like to be proved, then the answer is the following. The Mendeleev table claims, for example, that the first elecctronic orbit can have only 2 electrons, the second - 8, the third - again 8, the fourth - 18, and so on. Another regularity is the structure of subshells. If quantum mechanics was an axiomatic system, all those regularities would be proved. I asked, whether this is indeed so. And it is strange for me that there are mathematicians who say that this question is unclear or incorrect.
Nov
7
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: 1) There is only one preson, who can explain what Jacques Carette had in mind - this is Jacques Carette himself. Instead of disputing what he wanted to say, it is much more clever to ask him this question. I did exactly this. Before he gives an answer it is senseless to refer to him. By the way, do you think it was nice of him that he dropped a hint, and disappeared immediately after that?
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Mark: there was no necessity to remove your coments here. However, I appreciated your will to talk to me, but you see, the discussion could be much more interesting, if you didn't close this topic so quickly.
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Dmitri: 1) I asked Jacques Carette what he has in mind - he did not reply. If his suggestion was more clear, I would consider it more seriously. 2) Your reformulation of my question is not correct: I am asking about axiomatization of quantum mechanics. Formally this is not equivalent to finding eigenvalues or eigenfunctions of Schrödinger operator, since one could expect that the Mandeleev table could be proved without considering those eigenvalues. My question is absolutely clear and correct for mathematicians who have an impression of what axiomatic system is, why I should reformulate it?
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Mark: I guess, this means that you do not think I am a mathematician. You can check this by the link I gave at my page here: mathnet.ru/php/… Is "Doctor of Physical and Mathematical Sciences" enough high level for you?
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Mark: from this discussion it follows that there is a qualitative difference between mechanics (as a part of differential geometry) and quantum mechanics (as a part of what you say): in the first case this is an axiomatic system, while in the second one this is not. And this is not obvious for non-specialists like me. So, when appealing to colleagues, I thought I could count on their understanding, since they at least are able to understand my question. But what I see here from moderators is not called understanding, this much more resembles rudeness ("hamstvo" in Russian, is it? :).
Nov
6
revised Topology on the space of Schwartz Distributions
deleted 2 characters in body; added 4 characters in body
Nov
6
comment Topology on the space of Schwartz Distributions
Of course, compact-open topology on the space of operators is locally convex. But not likely nuclear, barreled or Frechet... Maybe for operators on S this is true, but I do not know.
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Mark: 2) concerning this: "There is no option "question does not make any sense" in the list of closing options." -- It is not me who pretend that quantum mechanics is based on "postulates", so this is pulery mathematical (if you want, logical) question, if this pretension can be considered as a presentation of an axiomatic theory. Doesn't this make sense?
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Mark: 1) if physicists did not convince me, like Luboš Motl at their physical forum, that everything is "fully, quantitatively, and comprehensively" explained, I would not ask this question here. But their arguments are always so definite, uncompromising, unequivocal (and I would say in some sense offensive, don't you find them so? :), that you begin to think that maybe you read wrong books, and if you ask mathematicians who are interested in tags like "quantum-mechanics", they will give an explanation, which could be verified (as this usually happens with mathematicians).
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Greg: 2) will the following revision of my question be suitable: "should we treat the postulates of quantum mechanics as axioms of an axiomatic system?"
Nov
6
comment Is the Mendeleev table explained in quantum mechanics?
@Greg: 1) if you ask this "great chemistry-and-physics question" to chemists or physicists, they will treat you as an idiot (and this is what happened to me at theoreticalphysics.stackexchange.com/questions/473/… ). Because they do not understand what logic is. If this were not so, there would not be contradictions between what people write here and what they write there: "Yes, quantum mechanics... – fully, quantitatively, and comprehensively explains all of chemistry..." So I still think that I should address this to mathematicians.
Nov
5
answered Topology on the space of Schwartz Distributions
Nov
5
comment Is the Mendeleev table explained in quantum mechanics?
"closed as off topic by Greg Kuperberg, Mark Sapir, Todd Trimble, Ryan Budney, Alain Valette 30 mins ago" @ Greg Kuperberg, Mark Sapir, Todd Trimble, Ryan Budney, Alain Valette - gentelemen, may I ask you, why did you decide that this is off topic?
Nov
5
comment Is the Mendeleev table explained in quantum mechanics?
Terry, thank you very much for your answer, but your link is just a presentation, it does not contain even references... I would like to thank also the other people who wrote the answers. So, dear colleagues, as far as I understand, we came to a conclusion that from the point of view of logic the Mendeleev table is not explained in quantum mechanics? :)