Talk:Hamiltonian (quantum mechanics)

message: 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)
replies: text: I think you mean written using. Written in would refer to the language, but if you mean the structure and syntax, written using such appallingly poor English would be more appropriate. DareManWin (talk) 12:10, 22 March 2024 (UTC)
thread_title: Quality of English

message: Which is it? 
\hat{H}=-\frac{\hbar^2}{2}\left( \sum_i \frac{1}{m_i} \nabla^2_{\mathbf{r}_i}\right) + V(\mathbf{r}_1,\ldots ,\mathbf{r}_N,t)
or
\hat{H}=-\frac{\hbar^2}{2}\left( \sum_i \frac{1}{m_i}\nabla^2_{\mathbf{r}_i} + \frac{1}{2}\sum_{i\neq j} \frac{1}{m_i+m_j}\nabla_{\mathbf{r}_i}\cdot \nabla_{\mathbf{r}_j}\right)+ V(\mathbf{r}_1,\ldots ,\mathbf{r}_N,t) ???
(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)
replies: text: The former is the correct one in typical canonical coordinates. Cross terms in the kinetic energy can appear if one e.g. uses relative coordinates (see e.g. https://physics.stackexchange.com/a/80719)  — Preceding unsigned comment added by 130.153.73.30 (talk) 07:37, 4 January 2018 (UTC)
thread_title: Cross terms for kinetic energy?

message: 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? 
:"Total energy" just means kinetic + potential energy. Why don't they just call it energy and be done with it? It's because the motion of bodies is calculated a different way. Normally, we use Newton's law F=ma, and we can say that a body of mass m moved with this trajectory because ot was accelerated by these forces. If we want to calculate the energy total energy = sum of potential and kinetic energies, we can derive it from the speed of the body, and it's movement against the forces. However, you could derive the trajectory of the body a completely different way: use your knowledge of the total energy of the body. If it was a bead moving along a wire, you might know that the total energy is constant. It would be hard to use Newtonian mechanic to calculate what the bead will do. The alternate way of calculating it is called Hamiltonian (classical) mechanics, and the Hamiltonian is just the energy, as I said. But we came at the problem from a different direction, so historically "energy" here has a different name - "hamiltonian". 
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)
thread_title: Total Energy?

message: # "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? 
# "The eigenkets" — link to Bra-ket notation? Explain the relationship with Bra-ket notation?
# "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?
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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
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#The Hamiltonian is the operator, not the system itself, so this change would be incorrect.
#Bra-ket notation has nothing to do with the Hamiltonian specifically, but that link will be for people who haven't come across bra-ket notation yet.
:Marbini (talk) 23:29, 27 August 2009 (UTC)
thread_title: Some questions

message: 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)
replies: text: thanks for pointing it out. that link has been removed. Mct mht 15:27, 10 December 2006 (UTC)
thread_title:  "Free States" article has nothing to do with quantum states. 

message: 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)
replies: text: Have a look here. --TraceyR (talk) 11:22, 16 May 2009 (UTC)
thread_title:  Eigenket? 

message: The above Irish mathematician seems to be ignored throughout Wikipedia wherever the term "Hamiltonian" is used. --TraceyR (talk) 11:18, 16 May 2009 (UTC)
thread_title:  Sir [[William Rowan Hamilton]] 

message: 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)
replies: text: Re "if you ask me.  I think this statement may be someone's misunderstanding.": Yes, that is not correct. The Hamiltonian itself is the energy observable. Mct mht (talk) 17:42, 1 July 2009 (UTC)

text: Agreed. I'll try and clean the introduction up a bit now. Marbini (talk) 23:33, 27 August 2009 (UTC)

text: I concur. Perhaps some of the words can become links?
 bi  — Preceding unsigned comment added by 42.106.85.153 (talk) 15:11, 9 October 2011 (UTC)
thread_title: Definition at the top

message: Under "Schrodinger formalism", shouldn't the kinetic energy be given as below?
\hat{T} = \frac{\mathbf{\hat{p}}\cdot\mathbf{\hat{p}}}{2m} = \frac{\hat{p}^2}{2m} = -\frac{\hbar^2}{2m}\nabla^2
Fixed.--Maschen (talk) 17:39, 8 January 2012 (UTC)
thread_title:  Sign error? 

message: What is the significance of the following notation variants in this article:
* hat vs no hat (on H for example)
* bold vs not bold on various variables
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)
thread_title:  Notation question 

message: 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)
replies: text: That raises a fair point, the classes are taken simultaneously. There is, however, always some introduction to the classical concept before diving straight into operators, in my experience. I have withdrawn that request due to pushback and changes made in the DAB page itself. Footlessmouse (talk) 01:18, 2 November 2020 (UTC)
thread_title:  classical and quantum teaching 

message: 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)
thread_title:  Define variables