Talk:Tight binding

Would the "tight binding" approximation, being based, on isolated atomic orbitals, be expected to fail, at super-high pressures & densities, e.g. in the cores of planets ?? 24.143.65.75 (talk) 01:15, 30 January 2012 (UTC)

Point that could use correcting

The article, while very slightly helpful right now, really needs the actual derivation of the energy levels. I cannot, for the life of me, find this anywhere. I'm going to go try ashcroft and mermin, but otherwise I'm stuck :(

Point that could use clarification

I'm under the impression that there's some relationship between this article and the article Linear combination of atomic orbitals. But neither article explains that relationship. Could someone add that information if they know it? Or, if appropriate, merge the two articles? --Steve (talk) 03:36, 17 August 2008 (UTC)

I'm learning about this right now, I'll reword this article when I understand this model better. There are some blatent mistakes where they make it sound like the wavefunctions and the atomic orbitals are the same thing. I'll rewrite some of this later.Bridger.anderson (talk) 20:10, 9 February 2009 (UTC)

Atomic orbitals are valid wavefunctions. If two atoms are nearby, their respective orbitals will noticeably deviate from orthogonality. Still, an electron wavefunction can definitely coincide with an atomic orbital. Yes, I know you mentioned this almost two years ago. -- Luke Somers, 19 December, 2010

This article is a mess

Besides poor organization, bad grammar, and failure to define notation, this entire article is a mess. As one example, the statement is made that this approach is an approximation to the Hamiltonian, while in fact it is only an approximation to the wavefunction. Brews ohare (talk) 23:28, 27 May 2009 (UTC)

It might be added that the viewpoint of this article, that the tight-binding wavefunction is to be seen as an approximate implementation of Wannier functions, is overly restrictive, because, like the LCAO method, the tight-binding method is not restricted to periodic lattices, while Wannier functions are so restricted. Brews ohare (talk) 15:30, 28 May 2009 (UTC)

I've seen people teach tight-binding as an finding approximate solutions to the true Hamiltonian, and I've seen people teach it as approximating the Hamiltonian and then writing down its exact solutions. Either presentation can be correct, it's a rather meaningless distinction anyway. --Steve (talk) 18:40, 28 May 2009 (UTC)

I agree with Sbyrnes321. Form the first principle calculation point of view, tight binding method means to expand the single particle Hamiltonian in the Wannier function basis. But in condensed matter physics, tight binding model means to approximate the kinetic energy term in the Hamiltonian by hopping terms that transfer electron from site to site. In this sense, tight binding approximation can be understood as an approximation of Hamiltonian indeed.Everett (talk) 21:00, 15 February 2011 (UTC)

Tone of history

It may be accurate, but the statement that the 1950s paper is the 'absolute climax of the history of the tight binding model' seems to me to violate the neutral tone guideline. -- Luke Somers, 19 December, 2010

Error in the equations

The first equation in the section "Mathematical formulation" is wrong! The first term on the right hand side actually gives the full Hamiltonian for the solid without the need of the last term (delta U). In the tight binding approximation one separates out the term H_atom at a given lattice point and put the rest of the hamiltonian in a term delta U which is assumed to be small. A general tidying up by someone well versed in this are is needed for this article. — Preceding unsigned comment added by 2001:660:2402:14:FA1E:DFFF:FEDA:FF88 (talk) 11:01, 25 February 2013 (UTC)

Needs much more use of second quantisation notation

Although it is a bit harder to grasp conceptually, second quantisation notation makes tight-binding a lot less difficult to read, and has a lot of power behind it. Moreover, this *is* the language that this is used in these days, in textbooks and papers and in classes. I think most of this article needs to be rewritten to be helpful to people new to the topic rather then just plain confusing. 130.102.158.24 (talk) 13:07, 17 May 2013 (UTC)

I do not agree. The idea that people new to the topic will find second quantisation notation helpful is, I suggest, not correct. It is much better to start the equations, as the article now does, with the LCAO approach. Many people will be coming new to the topic from a chemistry background, given the increased chemistry interest in solids. Chemists rarely understand the second quantisation notation. I think the present approach is about right, with a long introduction that uses no equations, followed by a LCAO approach, and then the second quantisation notation. Each of these sections of course is open to improvement, but please do not try to explain it only using second quantisation notation. --Bduke (Discussion) 22:12, 17 May 2013 (UTC)

Possible upgrade to the importance of this page

I think this page deserves at least a 'mid' importance rating, if not a 'high' - I would think every physicist in condensed matter (which is the largest branch of physics) would have seen this, and I encountered it in my undergraduate course in Australia. 130.102.158.24 (talk) 13:07, 17 May 2013 (UTC)

Here, I agree. It should be 'mid' but not 'high'. I have been bold and changed it. --Bduke (Discussion) 22:12, 17 May 2013 (UTC)

The Mathematical Formulation section is wrong.

The full Hamiltonian is *not* the sum of the isolated atomic Hamiltonians. Since each atomic Hamiltonian contains the kinetic energy, as written, the full Hamiltonian contains the sum over the lattice of the kinetic term, hence $\infty \times T$... Topologicalinsulators (talk) 08:54, 25 June 2020 (UTC)

I will come back to correct this, referring to Ashcroft and Mermin. Topologicalinsulators (talk) 08:54, 25 June 2020 (UTC)

Possible wrong factor in the one-dimensional example

On section "Example: one-dimensional s-band" I fail to see the reason why there is a factor 2 in front of the cosine rather than a factor 4 in the expression of $\langle k|H|k\rangle$. If I am not mistaken, there is a factor 2 coming from the $n\pm 1$ states, whose integrals both yield $-\Delta$, as expressed earlier in the text, but another factor 2 coming from expressing the sum of exponentials as a cosine.

I do not have access to the source cited in that section, so I will not edit it in case I am indeed wrong. I would love to hear anyone else's take on the matter, though. --Kakahuete (talk) 22:57, 11 May 2021 (UTC)

Possible wrong statement

The statement about swapping orbital indexes confuses me. It seems that swapping indexes could result in inverting the sign of the Hamiltonian matrix element. If this is the case, the Hamiltonian is not a symmetric matrix (Hermitian if the numbers involved are complex), therefore its eigenvalues would not be real numbers. 80.221.180.9 (talk) 14:00, 1 March 2024 (UTC)