Consider a deuterium atom (composed of a nucleus of spin 1 and an electron). The electronic angular momentum is J = L + S, where L is the orbital angular momentum of the electron and S is its spin. The total angular momentum of the atom is F = J + I, where I is the nuclear spin. The eigenvalues of J2 and F2 are J(J+1)h2 and F(F+1)h2 respectively.
(a) What are the possible values of the quantum numbers J and F for a deuterium atom in the 1s ground state?
(b) What are the possible values of the quantum numbers J and F for a deuterium atom in the 2p excited state state?
The muon is a heavy
electron which is identical to the electron except that it has a rest mass mm=207me , where me
is the electron mass. The muon is unstable and it can decay into the final state 
are massless particles of spin ½ , which are
called the electron antineutrino and muon neutrino respectively. They may be considered
non-interacting with ordinary matter in what follows. Because the muon has the same charge
as the electron, it can form an atom with the proton, which we denote by Hm. Consider the ground state of Hm.
(a) What is the ground state energy E0
m of Hm.(b) Suppose in the ground state of H
m the muon decays at time t = 0 into
such that the
3-momentum 
Find the probability that the
electron is in the ground state of ordinary hydrogen at t>0.
The following wavefunctions refer to the hydrogen atom.
(a) 
( eigenfunction of H, L2,
Lz, Sz )
(b) 
( eigenfunction of H. L2,
J2, Jz )
For each eigenfunction calculate 
The three
matrices, Mx, My, and Mz, each with 256
rows and columns, obey the commutation rules 
The eigenvalues of Mz
are ±2h
(each once), 
(each eight times), 
(each 28 times), 
(each 56 times), and 0 (70 times).
State the 256 eigenvalues of the matrix
M2=Mx2+My2+Mz2.
A particle of spin
½ is in a D-state of orbital angular momentum. What are its possible states of
total angular momentum? Suppose the single particle Hamiltonian is 
What are the values of energy for each of the
different states of total angular momentum in terms of the constants A, B, and C?