Basically, I've written some code that take as inputs 1)Basis vectors 2)lattice translation vectors
and computes the structure factor of the basis, producing a diffraction pattern.
I'd like to begin incorporating subtle differences between atoms, so I want to compute the structure factor of...
I'm writing a little bit of Mathematica code that should be able to make a reasonable powder diffraction spectrum. The algorithm is like this:
Take Bravais lattice and basis. Compute reciprocal vectors.
Compute structure factor (and its square magnitude)
Have triple nested loop that creates...
Hi, PF. I've got a question for you. Maybe this would be better posted in the science education or discussion sections, but it's directly related to QM. I'm just finishing up my undergrad coursework and I've taken QM using Griffiths. It's an okay book, but it does a bit of jumping around, and...
The variable is ##x##, so make the given equation look like a regular quadratic in ##x##. Then pick off what ##a##, ##b##, and ##c## are and write the inequality for ##\Delta## in terms of those. It will quickly resolve into what's requested.
I believe that's correct. And you can always plug your function for y back into the differential equation and make sure that it gives you a true statement.
It's should be arctan(x). So
$$
y'\arctan(x)-\frac{y}{1+x^2}=0\\
\Rightarrow \int \frac{\mathrm{d}y}{y}=\int \frac{1}{1+x^2}\frac{1}{\arctan(x)}\, \mathrm{d}x\text{.}
$$
At this point it is helpful to note that
$$
\frac{\mathrm{d}}{\mathrm{d}x}\arctan(x)=\frac{1}{1+x^2}\text{.}
$$
So...
There are some cool ones in here:
http://homepage.mac.com/stevepur/physics/matter/matter.3.html
http://oer.physics.manchester.ac.uk/NP/Notes/Notes/Notesse30.xht
$$
k=\pm i
$$
So the general form of the solution is
$$
Q_g(x)=c_1 e^{ix}+c_2 e^{-ix}
$$
Or equivalently,
$$
Q_g(x)=A\sin(x)+B\cos(x)
$$
Now take a guess at the particular solution. Let's guess that ##Q_p(x)=D\sin(2x)##. Plug this into the differential equation and solve for D. It...