22.51 Quantum Theory of Radiation Interactions
Problem set # 4
Issued on Monday Oct 22, 2012 . Due on Monday Nov. 5, 2012
Problem 1:
NMR relaxation
Consider an ensemble of spin-1/2 particles (a liquid NMR sample) in the presence of a static inhomogeneous

22.51 Quantum Theory of Radiation Interactions
Problem set # 5
Issued on Wednesday Nov 7, 2012. Due on Wednesday Nov. 21, 2012
Problem 1:
Displacement operator
The operator D(z) = exp(za z a), for a harmonic oscillator or a single-mode eld, is a displacem

22.51 Quantum Theory of Radiation Interactions
Problem set # 3
Issued on Wednesday Oct 10, 2012. Due on Monday Oct. 22, 2012
Problem 1:
Trace of tensor products
Take a tensor product space H = A B of dimensions m n and consider two operators A A and B B.

22.51 Quantum Theory of Radiation Interactions
Problem set # 1
Issued on Wednesday Sept. 12 2012. Due on Monday Sept. 24, 2012
Problem 1:
Pauli matrix vector space
a) If A and B are matrices of the same dimensions, show that hA, Bi = T r[A B] has all the

22.51 Quantum Theory of Radiation Interactions
Problem set # 6
Issued on Tuesday Nov 27, 2012. Due on Friday Dec. 7, 2012
Problem 1:
The dipolar approximation
We have seen in class that the Hamiltonian for the interaction of atoms and radiation elds is gi

22.51 Quantum Theory of Radiation Interactions
Problem set # 2
Issued on Monday Sept 24, 2012. Due on Monday Oct. 8, 2012
Problem 1:
Neutron Interferometry
|U
|L
BS
1
BS 2
Figure 1: Neutron Interferometer
Consider a neutron interferometer (NI), such as th