Well, terms with an odd number of operators are out immediately if the particle number is conserved. The two-operator term represents direct hopping, the lowest-order process, which presumably is the most important one. You can of course imagine an electron hopping from site 1 to site 2 and then...
You're right. I guess I should have said that the wave function must be square integrable and satisfy all other physical conditions of wave functions. (It certainly would be weird if the probability of finding the particle infinitely far away is non-zero.)
The idea is that the wave function must be square integrable, so it must fall off to zero faster than functions which aren't.
Or put another way, integrate \left( 1/\sqrt{|x|}\right)^2 and see what you get.
Ok... To be honest, that is a bit of a red flag! QFT is a tricky subject in its own right, but it relies heavily on classical mechanics. So you may want to pick up a good book and learn Lagrangians, variational calculus and Noether's theorem properly as soon as possible. Otherwise I think you...
As Peskin and Schroeder present it, the calculus is essentially that of partial derivatives while treating \phi and \partial_\mu \phi as independent variables. For a given Lagrangian density \mathcal{L}, he defines the current in eq. (2.12). However, the current depends on the symmetry at hand...
You may want to read http://www.scientificamerican.com/article/reading-paper-screens/
Basically, there may be some advantages to reading on paper, in terms of long-term retention etc. Searchability is a big argument for ebooks, but for textbooks I think it is overrated. If one needs to look...
You don't need to calculate it directly, though it is a good exercise.
First, recall that the hopping term looks like c^\dagger_{i,\sigma} c_{i+1,\sigma} (specializing to 1D for simplicity) and assume that we start at half-filling. If we assume (like Altland and Simons do) that U\gg t, then...
Can you be more specific about where you are having a hard time? Is it the change of coordinate system?
Also, when asking a question like this, it's quite reasonable to mention that you're setting h_p=h=h_s=0. Makes it easier to relate your equations to those in the paper.
Well, I'm not sure how sensitive DFT is to these things or how the specific material is supposed to behave, but in other simulations one often needs to pay attention to boundary conditions (you can check if you have an even-odd effect when changing cell size) and to finite size effects. For the...
The main issue with your first question is that there isn't really such a model. Or rather, one can only write something like H_{tot}=H_e + H_I + H_{int} where H_{tot} is the total Hamiltonian, H_{e} is the electron Hamiltonian which contains the kinetic energy of each electron and all...
I'm not familiar with this particular model, so I don't know the connection with the fractional quantum Hall effect or the eigenstates. However, it seems quite clear to me that while the spins themselves are at fixed positions, the dimerized bonds are free to move (as in changing which spins are...
Yeah, it has to do with stacking. There are several notations, of which I'm most used the ABC one myself. However, I think this is Ramsdell notation, in which H=hexagonal and the number two would signify the number of layers. Hence 2H should correspond to AB stacking, which agrees with the...
Hi,
You apply and say you will need funding. Then they decide whether to accept or reject you, while also giving you information about the funding they choose to offer you (they will most likely include the tuition fees). Nothing else is certain.
This seems more like a math question to me (I've only seen it in functional analysis), but anyway. In this (and most cases), \Subset tends to be used as an alternative to (the in my opinion rather ugly) \subset\subset, and means that one set is compactly contained (or embedded) in the other. For...
The hydrogen eigenstates have specific angular momenta, so they must be eigenstates of the angular momentum operator. Does that operator commute with the position operator? Also check ChrisVer's point, does position really commute with the Hamiltonian in this case?