Take-Home Test 1

 

Problem 1:

An electron in a state of the hydrogen atom with n=3, l=2 has total angular momentum 5/2.  Find the ratio of the expectation values of z in the eigenstates of Jz with eigenvalues 5/2 and 3/2.

Given:

Problem 2:

A neutron is bound in a square well potential of range 1.4fm and depth 400MeV.  Find the binding energy of all the possible S-wave bound states.

Problem 3:

Suppose that the muon replaced each electron in all atoms.  If the ratio R=mm/me»200, by what power of R, if any, would the following quantities scale?

Size of a typical atom
Binding energies
Density of matter
Effective spring constant in diatomic molecules
Typical vibrational energies in diatomic molecules
Typical rotational energies in diatomic molecules

Problem 4:

Evaluate the ratio R of the difference in energy of the first two rotational levels to the energy difference in the first two vibrational levels for the HF molecule. The moment of inertia of HF is equal to I=1.35´10-40g-cm2 and the vibrational frequency is equal to Dnvib=3987cm-1.

Problem 5:

We are to add angular momenta j1=3/2 and j2=2 .

  1. What are the possible values for j?
  2. Express all eigenkets |j1,j2;j,m>=|3/2,2;3/2,m> in terms of |j1,j2;m1,m2>.
  3. Express the ket |j1,j2;m1,m2>=|3/2,2;1/2,0> in terms of |j1,j2;j,m>.
  4. What are the expectation values of J1z and J2z in the state |j1,j2;j,m>=|3/2,2;1/2,1/2>?