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?
The m files work as functions, so all you need to do is to call that function. I.e., if you called the file game.m, just replace the fprintf('I do not know how to restart, sorry!\n\n') by game
EDIT: That will restart the script right from the beginning. If you want it to restart somewhere else...
Glad you solved it.
I find optimizing Mathematica code tricky, as there generally is several ways of doing the same thing, and it's often not obvious why one should be quicker than the other. Anyway, there's this guide 10 tips for writing fast Mathematica code. You might find it helpful too.
You want to tell Mathematica that your functions are to be treated as functions,
g[b_, c_] := b/c
f[a_, b_, c_] := a*g[b, c]
Note the underscores after the function variables.
Also see the tutorial.
You do realize that physics is all about coming up with these rules to describe and predict the way the world behaves, right? That is the scientific way. Usually the rules take the form of equations (though it's not obvious a priori why mathematics should be useful at all). Sometimes we can...
I'd guess that "com an-bound val" stands for complex analysis and boundary value problems, or something similar. On the other hand, it is not clear to me whether a course with that name would focus on (useful) complex methods for solving differential equations, or on equations with solutions...
I think, at least in some models, the antenna itself is rotating. Whether that is better or not, I don't know - still using a turntable variant here. Though it seems that these models are very hit or miss, so make sure to read the reviews on that specific microwave first.
As far as the Zeeman effect and magnetism goes, I think people often tend to think of spin as a classical vector which points in some direction. It's not strictly right, but for many intents and purposes it works just fine as one tends to be more interested (at least in these applications) about...
Generally, one would treat the case of R=0 separetely, and solve the differential equation for this case too, which is obviously permitted. Your method is essentially the same, if one matches the solutions using the smoothness property (the derivative of the wave function is continuous too)...
It's quite tricky to find a simple and general criterion, but I remember seeing it be done for classes of equations, e.g. diffusion equations. If you are looking for a general answer, it probably will have something to do with symmetries and be rather distanced from how physicists would tend to...
That output looks right for that code. Let's look at your two cases to see what the program actually does.
If p=9, p/2=4 (remember integer division). Due to the test in the for loop, you will test the values i=2 and i=3. In the case of i=2, 9%2=1 and it prints prime no matter what the later...
What is going on is essentially this: Suppose you are integrating a constant (equal to unity for convenience) from x=1 to x=0 along the x axis. Would you say that because we are moving in a negative direction, dl=-dx, and thus
\int_1^0 dl = -\int_1^0 dx = 1
or would you just say that the...
Hi,
I think he tends to be mentioned whenever authors give an overview of the history. As an example, the only two QM textbooks I have available right now, Sakurai's (standard) book and Weinberg's "Lectures on quantum mechanics", do mention him and his role when it came to matrix mechanics...
Aha. Yeah, I wondered if the product solution was too simple to suggest but then I remembered that I once spent an hour perfecting a recursive algorithm in java to format a text string before someone reminded me that I could just have used a string replace function.
Nice solution, by the way.