Recent content by Proofrific

Thanks! That answered my question. For others, if a+b+c = 0, or a+b-c=0, or a-b+c=0, or a-b-c=0, then we integrate cos(0) = 1 and get 1/4.

[solved] Integral of Product of Three Cosines I'm trying to determine the integral of the product of three cosines: \int_0^\infty \cos \left( \frac{n \pi t}{T} \right) \cos \left( \frac{m \pi t}{T} \right) \cos \left( \frac{l \pi t}{T} \right) dt for n, m, l integers. Some of the results...

Whoops, sorry. I meant v = r \omega, but you did that right. My bad. I don't see any problems with what you did. It looks like you did it right. Perhaps the solution is wrong?

Check how you went from angular velocity (w) to translational velocity (v).

Homework Statement A particle is moving in a potential V(R) = \frac{1}{2} \left( \frac{1}{R} - \frac{1}{R^2} \right)^2. If you plot this, is has a well at R = 1 with height V(1) = 0 and a hump at R = 2 with height V(2) = 1/32. Question: If a particle has energy 1/32, show that it takes...

Thanks for the help! How do you know that L_zr=L_z\theta=0? The only thing I remember about L_z is how it acts on an eigenstate: L_z|l,m\rangle = m \hbar | l,m \rangle. How do you know how it acts on r, \theta, and \phi?

Homework Statement It's not a homework problem. I'm reading my textbook (Sakurai's Modern QM), and I'm not sure about a step (eq 3.6.6 through 3.6.8). Here it is: We start with a wave function that's been rotated: \langle x' + y' \delta \phi, y' - x' \delta \phi, z' | \alpha \rangle Now...

I'm getting two different radial equations depending on when I plug in the angular momentum piece. Here's the Lagrangian: L = \frac{1}{2} \mu (\dot{r}^2 + r^2 \dot{\phi}^2) - U(r) The Euler-Lagrange equation for phi gives angular momentum (conserved), which can be solved for \dot{\phi}...

I'm not sure how to determine the "meaning" of a problem I'm working on. It comes from calculus of residues, where I'm trying to evaluate the integral: \int_0^\infty \frac{x^{\mu-1}}{x + 1} dx . So, I'm using the complex integral \oint \frac{z^{\mu-1}}{z + 1} dz , where the cut line...

I'm going to assume that the particle acts like a mass on a spring. Then, we can solve this problem using conservation of energy. At the system's biggest displacement (3cm), there is no kinetic energy, so the total energy of the system is just the energy from the spring: E_{tot} =...

I have two ways of evaluating (e^{i 2 \pi}) ^{1/2}, and they give me different answers. Which one is correct, and why is the other wrong? Method 1: (e^{i 2 \pi}) ^{1/2} = e^{i \pi} = -1 Method 2: (e^{i 2 \pi}) ^{1/2} = 1^{1/2} = 1

I have a question about why \left. x \left( \Psi^* \frac{\partial \Psi}{\partial x} - \frac{\partial \Psi^*}{\partial x} \Psi \right) \right|^{+\infty}_{-\infty} = 0. I understand that normalization requires that \Psi goes to zero at \pm \infty. But, what about the x in front of the...