Physics 721: Homework # 5 Solutions
1. Beam splitter transformations
Part 1: Show that aout = U 1 aU and out = U 1 .
Unitarity implies U 1 = U = ei(b
U 1 aU = ei(b
Using the equality
eA BeA = B [
Physics 721: Homework # 1 Solution Set
1. Optical transitions and angular momentum
(a) In abbreviated form, the Wigner Eckart theorem states that for an angular
momentum spherical tensor of rank 1, Jq , any set of operators Tq labeled by q that
Physics 721: Homework # 3 Solution Set
1. Raman Fluorescence
(a) The only relevant states are cfw_|1, 1k , |2 , |3 , since we can emit at most one photon
from this system (we could also include the state |1 with no photons present, but the
dynamics of the
Physics 721: Homework # 2 Solutions
1. Interference in spontaneous emission and quantum beats
a. Derive evolution equations for the amplitudes of the upper states c2 (t) and c3 (t).
In this problem we will work in the interaction picture where i | = V | .
Physics 721: Homework # 4 Solution Set
1. Bragg scattering
a. Derive the equations of motion for the probability amplitudes c1,p and c2,p .
The Hamiltonian describing the interaction of two elds of dierent frequencies and wavevectors (but the
same Rabi fr