Recent content by cscott

one bump

I made a typo in my boundary conditions Boundary conditions (in volts): V(a,\phi) = 2 \cos \phi V(b,\phi) = 12 \sin \phiTaking V(r,\phi)_{k=1} gives, V(r,\phi) = r(a_1 \cos \phi + b_1 \sin \phi)+\frac{1}{r}(c_1\cos \phi + d_1 \sin \phi) I will take a look at this...

Homework Statement Two coaxial cylinders, radii {a,b} where b>a. Find the potential between the two cylinder surfaces. Boundary conditions: V(a,\phi) = 2 \cos \phi V(b,\phi) = 12 \sin \phiHomework Equations Solution by separation of variables: V(r,\phi) = a_0 + b_0 \ln s + \sum_k \left[...

So because U has nothing to do with the magnetic field, I need to eliminate the vector potential from, \Pi_n \int \exp \left [-\frac{\beta}{2m_n} (\vec{p}_n - q \vec{A})^2 \right] d^3 p_n and change variable, \vec{u}_n = \vec{p_n}-q\vec{A} thus eliminating vector potential? Are the end...

Homework Statement Show that the free energy of classical particles with no internal magnetic moment is always independent of magnetic field. Hint: Write down Z for N classical particles. Let the particles interact by U which depends only on the positions of the interacting particles. Show...

Homework Statement Point electric dipole \vec{p}=p_0 \hat{z} is a distance d above an infinite metal plane of surface normal \hat{n}=\hat{z}. What is the force on the dipole. Is the dipole attracted to, or repelled from the surface?Homework Equations V(r) = \frac{\hat{n} \cdot \hat{p}}{4 \pi...

Homework Statement have band dispersion \epsilon = \epsilon_c + \frac{h^2 k_x^2}{2 m_x} + \frac{h^2 k_y^2}{2 m_y} + \frac{h^2 k_z^2}{2 m_z} Show density of states is g(\epsilon) = \frac{m^{3/2}}{\pi^2 h^2} \sqrt{2|\epsilon - \epsilon_c|} Homework Equations 2 \frac{d\vec{k}}{(2\pi)^3} =...

Thanks! I definitely thought about that too hard haha

Homework Statement H = -D(S^z)^2 for cases D>0, D<0, where D<0 should remove the degeneracy in the ground state.Homework Equations H = -D(S^z)^2 = -D\hbar^2 (1 0 0; 0 0 0; 0 0 1) (`;' separates rows) det(H-1E)= 0, or by inspection... The Attempt at a Solution I get, for D>0, E_1 = -D...

Homework Statement A hydrogen atom is placed in a time-dependent homogeneous electric field given by \epsilon = \epsilon_0 (t^2 + \tau^2)^{-1} where \epsilon_0,\tau are constants. If the atom is in the ground state at t=-\inf, obtain the probability that it ill be found in a 2p state at...

Homework Statement The time-averaged potential of a neutral hydrogen atom is given by V = \frac{q}{4 \pi \epsilon_0} \frac{e^{-\alpha r}}{r} \left ( 1 + \frac{\alpha r}{2} \right ) [tex]\alpha = 2/a_0[/itex], where a_0 is the Bohr radius. Find the charge distribution (continuous and...

One last bump... haven't gotten anywhere with this.

This was the thinking I was missing! So for H' = constant there is no first-order correction because l \ne n, yes?

Homework Statement A have a bit of a general question regarding 1st order wave function corrections using perturbation theory. In a problem like the infinite potential well where you have states numbered like n = 1, 2, 3, ..., how do you compute the sum for the 1st order correction when you...

did I state my question poorly? :\ This is problem 8.1 from B&J's book.