This is the talk page for discussing improvements to the Hamiltonian (quantum mechanics) article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
![]() | Daily pageviews of this article
A graph should have been displayed here but graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at pageviews.wmcloud.org |
Why are so many articles in this field written in such appallingly poor English? — Preceding unsigned comment added by 89.240.248.160 (talk) 17:46, 17 February 2023 (UTC)
Which is it?
or
???
(N-particle Hamiltonians)
Under what conditions is the latter more appropriate than the former? Where, mathematically, do these terms come from? This needs expansion. My text doesn't mention anything about cross terms. I would be very grateful for clarification!
24.22.53.72 (talk) 06:32, 10 April 2013 (UTC)
I came to this page looking for clarification on what my physics text states, however it falls into the exact same esoteric pattern. Exactly what does "total energy of the system" quantify? Further, the next sentence talks about variability in the total energy measured. Thus, in what sense is it total energy? Is it a probability distribution? An average?
Similarly, I think it's foolish that no where on the page can the equation H*Phi=E*Phi can be found. I know that equation is a huge simplification, but I think I can say with certainty that 80% of the people who come to the page will be most familiar with that equation given that it's frequently the first equation presented in Quantum classes having reference to the Hamiltonian operator.
Finally, I agree with the previous poster that this page has come down with "properties but not essence" syndrome, wherein the text rambles on about the properties of the subject but not the subject itself. If, as with many things in physics, it's difficult to describe it should be broken down into different conceptions or interpretations.
"total energy of the system" isn't jargon, it states the Hamiltonian of a system is the total amount of energy of the system. Besides lacking a definition of energy which is not approriate here.
In response to 3, it depends. Say your system consists of one particle with two internal states (say, "spin up" and "spin down") and some finite number n of possible positions. Then the particle has a total of 2n possible states, and your Hilbert space is 2n dimensional. However, if your particle can be anywhere in some region of space (i.e., it's not constrained to a discrete set of positions) then your Hilbert space will be infinite dimensional. Your Hilbert space also depends on how many particles are in your system, how many internal states those particles have, whether they're distinguishable or indistinguishable particles, etc.
If this is unclear, it should probably be clarified somewhere, but I'm not sure if it should be here or in the article on Hilbert spaces. The latter seems much more focused on the mathematical definition of a Hilbert space... although I think that's probably appropriate. Perhaps we could create a separate article (or subsection of that article) entitled "Uses of Hilbert spaces in physics" -- Tim314
I've not found the information I was looking for (what "Cauchy propagators" are). I think this is the wrong branch of QM; I need one of the time dependent formulations (?) such as Feynman's. Interesting, though, and worth reviewing before I try to understand that.
Mr. Jones 21:07, 1 Oct 2004 (UTC)
This page (like other pages that just jump into bra-ket notation) doesn't explain what the article's subject really is. Hyperphysics seems to suggest that the hamiltonian can be defined like this:
where U is potential energy.
Is this correct? Incorrect? Close? I have no idea how to read bra-ket notation (and the article on it doesn't help) - so I'm completely lost on this page, as I would guess that *most* people are who've come here. Fresheneesz 06:37, 30 April 2006 (UTC)
The text says that the spectrum ... is the set...., but the Wiki article for spectrum says that it represents a continuum, whereas, although not linked, the Wiki definition of set refers to "distinct things".
My guess is that spectrum is referring to some quantum mechanics definition, which is not presently in Wikipedia, so probably needs to be set (quantum mechanics) (broken at time of writing). I.E. it looks like an over enthusiastic wikification to me.
David Woolley 19:28, 13 November 2006 (UTC)
I am not really sure, whether you should give some definition of the hamiltonian without using fundamental concepts like hilbert space and diracs notation. The hyperphysics definiton is just a special case for 1D, 1 Particle etc... for the sake of unversality, one should use the proper notation, maybe with a comment like "If you are not familiar with Dirac-Notation click ->here<-" or something...
regards, sascha —Preceding unsigned comment added by 91.11.194.95 (talk) 11:34, 3 June 2008 (UTC)
I just noticed that the link to "Free States" takes you to a political page about governments and other such nonsense unrelated to the free states of particles in quantum physics. Don't know how to fix it, but there you have it.71.125.60.42 05:44, 10 December 2006 (UTC)
Shouldn't it be eigenkeit instead of eigenket? It's spread around the article and even appears in one of the headings. Sakkura 14:55, 30 November 2007 (UTC)
I've always heard eigenket- not that I've covered bra-ket notation in university yet but I read a lot, and have never come across the word eigenkeit- it's not a word I can find a translation for online either. I'm inclined to say it's a typo, as I think Dirac invented the notation and he certainly refers to them as kets.Marbini (talk) 16:14, 6 January 2008 (UTC)
Eigenket is correct, since it is referring to Dirac bra-ket notation.
Shouldn't the Hamiltonian be represented with a curly capital H? <math>\mathcal{H}</math> produces , which would appear to be the closest symbol available, and is used in the Hamiltonian mechanics article. Modest Genius talk 03:15, 16 October 2008 (UTC)
While this does not pertain directly to quantum mechanics, Jackson's electrodynamics text uses the script H as a Hamiltonian density (describing the Hamiltonian in terms of continuous fields rather than discrete coordinates), and reserves the typical H for the discrete Hamiltonian of point particles (and charges). 128.101.126.238 (talk) 05:27, 21 April 2009 (UTC)
Shouldn't there be some sort of link explaining the use of the vertical bar preceding and the arrow following the wave-function phi ? The meaning is not at all clear and therefore the article in its entirety is of little use. Could the author not correct this please ? —Preceding unsigned comment added by 92.236.77.63 (talk) 14:46, 21 November 2008 (UTC)
The above Irish mathematician seems to be ignored throughout Wikipedia wherever the term "Hamiltonian" is used. --TraceyR (talk) 11:18, 16 May 2009 (UTC)
Regarding this sentence at the beginning: "It is a Hermitian matrix, that, when multiplied by the column vector representing the state of the system, gives a vector representing the total energy of the system."
It gives a vector "representing" the total energy? Are you sure? In what way does this vector represent the total energy? As I understand it, the vector that it produces will be the sum of the total energy eigenstate components of the original vector, each multiplied by its corresponding total energy. Not much of a "representation", if you ask me. I think this statement may be someone's misunderstanding.
Also, a lot of people seem to be complaining that the page uses jargon and is inaccessible to laymen. While I agree with these statements entirely (as a neophyte the subject myself), and in other cases I sympathize, I can't imagine how you can make such a sophisticated and complex concept as a quantum operator accessible to a non-physicist. I mean, even physicists often struggle to completely understand these things at an intuitive level. This stuff is just plain intrinsically hard. What is the solution to such a problem? Should the page just be deleted? 24.174.30.146 (talk) 03:07, 25 June 2009 (UTC)
I really don't think the amount of "jargon" this page uses can be substantially further reduced without teaching people quantum mechanics. Should this tag really still be there? Marbini (talk) 00:25, 10 October 2009 (UTC)
bi — Preceding unsigned comment added by 42.106.85.153 (talk) 15:11, 9 October 2011 (UTC)
Under "Schrodinger formalism", shouldn't the kinetic energy be given as below?
Fixed.--Maschen (talk) 17:39, 8 January 2012 (UTC)
I realize that one often sees the the thing discussed in this article referred to as "The Hamiltonian", but names like this, in the obvious form of an adjective, cry out the question "Hamiltonian what?". The absence of that being spelled out propagates foggy confusion.
I gather from the article that the full name of the thing under discussion is "Hamiltonian operator", or "Hamiltonian function" (are these the same thing?), and to say so explicitly would be an improvement, I think.
There are apparently also Hamiltonian spaces, paths, matrices and so on. Any overview info that would help clarify which of these are related would be welcome!
By the way, the above point aside, I applaud the clarity of the first sentence "In quantum mechanics, the Hamiltonian is the operator corresponding to the total energy of the system." One question though: I wonder if the word "corresponding" is less precise than it might be: Are these other bolder sentences still correct:
If these aren't correct, then what does "correspond" mean?
Gwideman (talk) 11:09, 19 August 2012 (UTC)
I'm no expert, but the first and second sentences of the Introduction seem to me to say practically the same thing, or almost. Surely this badly needs editing. Seems that way to me anyway. AP — Preceding unsigned comment added by 58.109.71.99 (talk) 04:41, 1 September 2013 (UTC)
This sentence is probably wrong; It takes the same form as the Hamilton–Jacobi equation since the HJE is first order and non linear.. see this; https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation the Hamilton–Jacobi equation is written as a first-order, non-linear partial differential equation for the Hamilton's principal function {\displaystyle S(q,t)} Riadh A Rabeh. — Preceding unsigned comment added by 80.192.6.212 (talk) 19:37, 18 October 2019 (UTC)
What is the significance of the following notation variants in this article:
I appreciate that these variants may signify vector, normalized, array and so on, but it's sometimes not clear which meanings apply on this page, why they appear only sometimes, and indeed whether this page uses a particular convention consistently. Thanks. Gwideman (talk) 23:37, 14 September 2012 (UTC)
In general, a hat signifies it's a unit vector quantity, a small arrow pointing to the right just above the letter signifies it is a general vector quantity as does a bold symbol. Dots on top signify time derivates and a single quote after the symbol indicates spatial differentiation. If it is not bold and there is not vector symbol, it should be italic and that represents a magnitude. This is all universal notation. Footlessmouse (talk) 02:51, 2 November 2020 (UTC)
Discussion in talk:Hamiltonian suggests that in the usual schooling one should learn Hamilton's (classical) mechanics before the quantum mechanical Hamiltonian operator. As well as I remember, I had both courses at the same time, and am not sure in which order I actually learned them, or understood the connection. As is usual in many courses, the connections to other courses are often assumed, not taught, and often not quite learned. Is it really usual to teach Hamilton's mechanics before the quantum operator? Gah4 (talk) 01:07, 2 November 2020 (UTC)
Regarding g-factor, the article says: not to be confused with the gyromagnetic ratio. It seems to me, and I note on the Talk:Gyromagnetic_ratio page, the two are actually the same thing but with different units. That is, it is exactly the same physics. For the most part, we don't have separate articles for the same quantity but in different unit systems. Note, for example, that magnetic field includes both B and H, and we also don't have separate articles for tesla and gauss. Gah4 (talk) 12:31, 16 August 2022 (UTC)
V(r,t): what is r? This should be defined (so should t, although it is probably time). 129.2.192.123 (talk) 18:11, 7 March 2024 (UTC)