Recent content by Herr Malus

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.

You'll need to break the integrals into two parts. The first will integrate x+1 from -1 to 0, the second will integrate x-1 from 0 to 1.

When you use the wavefunction in the Schrödinger 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...

You're using the wrong method here, it seems. The method of characteristics you've set up is tailored to the case where the divergence of the function u is zero. Here it is not. Try something like a change of variables, to eliminate (say) y from your equation and reduce it to one variable.

To be honest, and I may have the wrong idea of the problem you're describing, it seems like your equation of motion is wrong. You'll have tangential and radial components for the acceleration. Radial should be more or less what you have, the v2/r term, but tangential should be something like...