課程名稱︰量子物理下
課程性質︰必修
課程教師︰侯維恕
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2008/04/02
考試時限（分鐘）：130 min (10:20~12:30)
是否需發放獎勵金：yes, thanks
（如未明確表示，則不予發放）
試題 :
Closed Book, Closed note (會發Eisberg量子物理課本前面的常數表)
1.(20pts)
(a) For multi-electron atoms, describe what LS coupling, and the physics
behind it.
(b) The 32Ge atom is in the lowest electronic configuration. Find all the
energy levels in spectroscopic notation, and identify the ground state.
(c) Use the weak external field approximation to deduce the Zeeman splitting
formula, and derive the Landé g factor. Show that the g factor lies
between 1 and 2.
(d) Draw the Zeeman splitting diagram for 3P2 of (b) in 0.1 tesla magnetic
field.
2.(20pts)
(a) Give plausibility argument for the Bose (Fermi) enhancement (inhibition)
factor when adding one more particle to n particles already in state α.
(b) Use principle of detailed balance at thermal equilibrium to deduce the
Boltzmann, Bose and Fermi distributions 1/Ce^(E/kT), 1/[Ce^(E/kT)-1],
1/[Ce^(E/kT)+1], respectively, with C ≡ e^α
(c) What is the principle of laser from photon perspective, and the key point
from the operational (atomic) perspective?
(d) Describe the principle of laser cooling.
3.(30pts)
(a) Explain under what conditions Bose condensation may occur.
(b) Plot the Fermi distribution at T = 0 and at kT = 0.1Ef.
(c) Conduction electrons inside a metal act like a Fermi gas. Use the T → 0+
limit to find the relation between Feermi energy Ef and the electron
density.
(d) Explain why the conduction electrons do not contribute to Cv at toom
temperature.
(e) Calculate Ef (in MeV) for a neutron star ～ 4×10^30 kg in mass
(twice m⊙) and 10 km in radius. Compare the gravitational energy at the
surface. Interpret.
4.(25pts)
(a) Explain how the pairing mechanism works for 3He superfluidity, and for the
covalent bond for molecular binding.
(b) Derive the rotational energy and the spacing rule for diatomic molecules.
(c) Give arguments for the scale of electronic, vibrational and rotational
energies, and argue why our atmosphere is transparent to visible light.
(d) The reciprocal wavelength for fundamental vibrations of H2, HD and D2 are
4395, 3817 and 3118 cm-1 respectively. Give a numerical explanation of
these differences, and how this was used historically to prove the
existence of zero point motion.
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