Time-dependent approximations
Addition of angular momentum, EM waves
Producing electromagnetic radiation
Relativistic E&M
Identical particles

Problem 1:

A hydrogen atom is known to be in a state characterized the quantum numbers n = 4, l = 2.
(a)    Give the allowed values of j.
(b)    For each of the allowed values of j, calculate the square of the magnitude of the total angular momentum.


Problem 2:

An electromagnetic wave with frequency 65.0 Hz travels in an insulating magnetic material that has dielectric constant κe = 3.64 and relative permeability κm = 5.18 at this frequency.  The electric field has amplitude 7.20*10−3 V/m.
(a)  What is the speed of propagation of the wave?
(b)  What is the wavelength of the wave?
(c)  What is the amplitude of the magnetic field?


Problem 3:

Consider an excited Nitrogen atom with a an electronic configuration (1s)2, (2s)2, (2p)2, (3s).
Find the spectroscopic terms 2S+1LJ that characterize the system.

Problem 4: 

A particle with mass m is confined to a 3D box.
V(x, y, z) = 0 if 0 ≤ x ≤ a AND 0 ≤ y ≤ b AND  0 ≤ y ≤ c,
V(x, y, z) = ∞ otherwise.
(a)  Write down expressions for the energy eigenfunctions and eigenvalues for this particle.
(b)  Assume that the particle is in the ground state of the system.  At time t = 0, all dimensions of the box suddenly double, i.e. a --> 2a, b --> 2b, c --> 2c.  A measurement of the energy of the particle is made just after the dimensions increase. (Assume that all this happens so quickly so the spatial wave function of the particle does not change).  What is the probability that the energy measurement yield a value EXACTLY the same as the energy of the ground state of original system?


Problem 5:

A non-conducting sphere of radius R = 0.1 m, mass M = 10 kg and uniform mass density carries a surface charge density σ = σ0cosθ, with σ0 = 10 microCoulomb.
(a)  Find the dipole moment p0 of the sphere.
(b)  Assume that at t = 0 the sphere receives an angular impulse and starts rotating about the x-axis with angular velocity ω0 = 1000/s.  Calculate the power radiated by the sphere when it rotates with angular frequency ω.
(c)  Estimate the time it takes for the rotation rate of the sphere to decrease by a factor of 2.


Problem 6:

Starting with the transformation of the electromagnetic fields under a Lorentz transformation show that
(a)  if E is normal to B in an inertial frame, it must be true in all other inertial frames, and
(b)  if |E| > c|B| in an inertial frame, it must be true in all other inertial frames.