Determine the energy levels and normalized wavefunctions y(r)
of a particle with zero angular momentum in a spherical "potential well" V(r)=0,
(r<a), V(r)=¥, (r>a).
Determine the average value of r and r2 for each of the energy
eigenstates with l=0.
Problem 2:
The n=3 to n=2 transition in hydrogen gives rise to the Ha line.
What is the wavelength of emitted photon?
Atoms are made up of nuclei consisting of protons and neutrons with masses Mpc2=938.280
MeV and Mnc2=939.573 MeV , and electrons with mass mec2=0.511
MeV. Suppose we lived in a hypothetical world, in which the masses of the nucleons were
unchanged, but the mass of the electron was 100 MeV. Assume in this world there is
no weak interaction, like the one in our world which is responsible for b-decay, such that
What is the wavelength of the Ha line in
this world? (You may ignore reduced-mass effects.)
In our world material densities lie in the range from 1 to 10g/cm3.
What is the range of densities in the hypothetical world? (You may ignore reduced-mass
effects.)
In our world many chemical reactions occur at temperatures of approximately 1000
K. What are the corresponding temperatures in the hypothetical world?
Show that if the weak interaction is allowed, the hypothetical world would have no
atoms.
Problem 3:
We are to add angular momenta j1=2 and j2=1
.
What are the possible values for j?
Express all eigenkets |j1,j2;j,m>=|2,1;1,m> in terms
of |j1,j2;m1,m2>.
Express the ket |j1,j2;m1,m2>=|2,1;0,0>
in terms of |j1,j2;j,m>.
What are the expectation values of J1z and J2z in
the state |j1,j2;j,m>=|2,1;1,1>?
Problem 4:
Determine the moment of inertia and the inter-nuclear distance of the 1H35Cl
molecule, if the difference in the frequency of two neighboring lines in the
rotational-vibrational (infrared) band of 1H35Cl is equal to Dn=20.9cm-1.
Evaluate the corresponding Dn for the DCl spectrum.
What is the wavelength of the Ha line in
this world? (You may ignore reduced-mass effects.)