课程名称︰量子物理下 课程性质︰必修 课程教师︰侯维恕 开课学院：理学院 开课系所︰物理学系 考试日期（年月日）︰2008/04/02 考试时限（分钟）：130 min (10:20~12:30) 是否需发放奖励金：yes, thanks （如未明确表示，则不予发放） 试题 : Closed Book, Closed note (会发Eisberg量子物理课本前面的常数表) 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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