Recent content by ultimateguy

Wow, I actually get it now. What a confusing problem!

I've seen this problem explained in the movie 21, as well as the show Numbers. I'll use the example given in 21. You're on a gameshow, and you're shown 3 doors. Behind one of the doors is a new car, and behind the other 2 are goats. You pick door number 1. The host then opens up door...

I worked for a particle physics experiment last summer. I have now just graduated and am supposed to continue working on that same project this Monday. I've determined that what I'm really interested in is medical physics. I just received an offer from a professor in medical physics to do a...

I've just finished up my undergraduate degree and I have been looking at graduate schools for an MSc. Unfortunately, due to my B average, I'm down to basically one choice, which is the institution that I'm presently attending. I've gotten experience in two fields in my undergraduate years...

Homework Statement For the potentials: V(\vec{r}, t) = ct \vec{A}(\vec{r}, t) = -\frac{K}{c} x \^x c being velocity of light in a vacuum, determine the constant K assuming the potentials satisfy the Lorentz gauge. b) Do these potentials satisfy the Coulomb gauge as well? c) Show that for a...

Homework Statement Consider an electron of a linear triatomic molecule formed by three equidistant atoms. We use |\phi_A>, |\phi_B>, |\phi_C> to denote three orthonormal staes of this electron, corresponding respectively to three wave functions localized about the nuclei of atoms A, B and C...

Yes I've seen it. So the eigenvectors are just for |\psi(0)> ?

Ok I found the two eigenvectors using Matlab. I'm not sure how to write them when applied to the system so that it makes sense. |\psi(t)> = 0.92388 | + > + 0.382683 | - > |\psi(t)> = 0.382683 | + > - 0.92388 | - > Is this correct? And for part c), which one do I use to find the probability?

Ok so I get the following system of equations for the case of the eigenvalue +\sqrt2 (1-\sqrt2)c_1 + c_2 = 0 c_1 + (-1-\sqrt2)c_2 = 0 which according to myself and my calculator has no solution...

Thanks, I found the problem, I should have had (1-\lambda)(-1-\lambda) = 1

For the eigenvalue: (\frac{B_0 \hbar}{2\sqrt2})^2 (1-\lambda)(1-\lambda) - (\frac{B_0 \hbar}{2\sqrt2})^2 = 0 (1-\lambda)(1-\lambda) = 0 \lambda = 1 And the eigenvector: \frac{B_0 \hbar} {2\sqrt2} \[ \left( \begin{array}{cc} 0 & 1 \\ 1 & -2 \\ \end{array} \right)\] \times \[...

So with this I get: H = \frac{1}{\sqrt{2}} B_0 \frac{\hbar}{2} \[ \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \\ \end{array} \right)\] + \frac{1}{\sqrt{2}} B_0 \frac{\hbar}{2} \[ \left( \begin{array}{cc} 1 & 0 \\ 0 & -1 \\ \end{array} \right)\] H = B_0 \hbar \[ \left(...

Homework Statement Consider a spin 1/2 particle placed in a magnetic field \vec{B_0} with components: B_x = \frac{1}{\sqrt{2}} B_0 B_y = 0 B_z = \frac{1}{\sqrt{2}} B_0 a) Calculate the matrix representing, in the {| + >, | - >} basis, the operator H, the Hamiltonian of the...

Thank you! I solved the problem.

The question asked to calculate the [H, XP] commutator, I just didn't write it because I already found it and wanted to save time. I'm not sure I understand the hint.