Talk:Hamiltonian (quantum mechanics)

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[edit] Total Energy?

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.

Per WP:JARGON terms that will not be understood by the average reader are especially important to define before they are used. I believe this is recursive, and introductory background is often paragraphs in length in similar articles. Listing Port (talk) 23:04, 9 April 2008 (UTC)

[edit] Some questions

  1. "In quantum mechanics, the Hamiltonian is the observable state of a system corresponding to the total energy of that system."
    • Is there anything wrong with phrasing it this way?
  2. "The eigenkets" — link to Bra-ket notation? Explain the relationship with Bra-ket notation?
  3. "Depending on the Hilbert space of the system" How do Hilbert spaces differ? How do they relate to the modeling of physical systems? Are the Hilbert spaces used here of infinite dimensions?
    • The relationship between the Hilbert space containing all possible states of the system (?) and the equation given is not clear. Where is the vector in this space?

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)

[edit] What is the hamiltonian?

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:

H = - \frac{\hbar^2}{2m} \frac{\partial^2}{(\partial x)^2} + U(x)

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)

I agree, this page does jump into rather technical definitions right away. People don't really need to understand Hilbert spaces to get an idea of what the Hamiltonian is. The hyperphysics definition is an appropriate one for a 1-dimensional system. In general, it's a measure of the total energy of the system - the first term above is the kinetic energy (simply p2 / 2m, see the article on momentum), and the second term is potential. KristinLee 00:28, 13 May 2006 (UTC)
The problem here isn't that the article isn't clear, simply that people are demanding you be able to read the text without having any knowlage needed to understant what an Hamiltonian is. Referencing hilbertspaces and dirac notation should be sufficient. The Hamiltonian in the link is one possible Hamiltonian, depending on what forces and interactions you include, the total energy of the given system be defined differently, and thus the Hamiltonian will change.
WP:JARGON has some different advice, which, it says, is particularly important for math articles. Listing Port (talk) 23:12, 9 April 2008 (UTC)

[edit] spectrum conflicts with set

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)

The term spectrum is used in a variety of contexts. Here, the term is probably borrowed from functional analysis but I don't think it should be thought of as a quantum mechanics term of art. In functional analysis, the spectrum of an operator is defined by its set of eigenvalues. The spectrum of an operator is sometimes discrete, sometimes continuous and sometimes a combination. Outside of quantum machinics, the term continues to be used in the same sense. A given operator may have various particular spectrums depending upon boundary conditions. In general fixed boundaries produce descrete spectrums and free boundaries produce continues spectra. (I hope you are still monitoring after the long wait for an answer!) --scanyon 06:14, 6 June 2007 (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)

[edit] "Free States" article has nothing to do with quantum states.

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)

thanks for pointing it out. that link has been removed. Mct mht 15:27, 10 December 2006 (UTC)

[edit] Eigenket?

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)