Well, the first is in the complex plane, C, so I'd assume dimension is 2. For the second, I think I actually want order (so I picked a bad example, my apologies), in which case it seems that the order is p-1.
Examples of the types of groups we're looking at are:
-"The set of Mobius transformations in the complex plane", where I assume the operation is composition.
-"The set {1,2,3,...,p-1} under multiplication modulo p, where p is a prime number."
If discrete is a reference to the discrete metric for a discrete topology, then yes. So in that case I assume we want a group of isolated elements. In differentiating between finite dimensional and infinite dimensional, are we just looking for the order of the group? I.e. the number n such...
I have a question regarding terminology here. The assignment is somewhat as follows: "If you think any of the following is a group, classify it along the following lines: finite, infinite discrete, finite-dimensional continuous, infinite-dimensional continuous."
The definition of finite is...
So using the Fourier transform would just give you the green's function for helmholtz in 3d space which is something like an exponential divided by 4∏r followed by simply any function satisfying the BC? So in a 1-d case:
Helmholtz Green's function + sinkx for x<x' or
Helmholtz Green's...
Homework Statement
Find the Green's Function for the Helmholtz Eqn in the cube 0≤x,y,z≤L by solving the equation:
\nabla 2 u+k 2 u=δ(x-x')
with u=0 on the surface of the cube
This is problem 9-4 in Mathews and Walker Mathematical Methods of Physics
Homework Equations
Sines, they have the...
I assume that your textbook (or resource or whatever) has the actual wave equation, and the procedure for solving i listed somewhere. I suggest you start there.
Now, as to some helpful hints if you don't happen to have that text available.
-In the problem statement, you noted that the...
If I remember correctly, this is the Laplacian in 2D, with azimuthal symmetry.
Edit: No, I'm wrong. Perhaps it has something to do with the 3D wave equation. I definitely saw this in a PDE course.
Same guy, yeah. Their response was to send the cops after him.
Wasn't there a boy scout who tried to do something similar (I think it was actually make a breeder reactor) in the US a few years back? I also seem to recall a very similar item (either splitting atoms or making reactors) on my...
When you use the wavefunction in the Schrodinger equation, it shouldn't matter what form (hyperbolic or exponential) you use. Your normalization is off however. The integral of sinh2(x) is:
Exponential form: \frac{1}{4} (exp(2x)/2+exp(-2x)/2-2x)
Hyperbolic form: \frac{1}{4} (sinh(2x) -2x)...
What's the problem with the Schroedinger equation? Are you using the time-independent version (I assume you should be), is there a potential energy associated with this wavefunction?
Further, the complex conjugate of a real valued function is just the real function again. So normalization...
The way you broke up the fraction is incorrect, you can't expand a minus sign in the denominator as you did. I suggest you start over, and this time instead expand the numerator with the identity csc2(x)=1+cot2(x). You will then find this problem to be significantly easier.
Depends on what you want to learn about ODE's, if it's the theory behind it then all I can suggest is Lebovitz's book (my only real exposure). On the plus side, it's free and he updates it as he teaches. He's also a pretty fantastic teacher in my opinion. If you want pure application then...