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）︰2008/5/14 考试时限（分钟）：10:20~12:30 (130分钟) 是否需发放奖励金：是，谢谢 （如未明确表示，则不予发放） 试题 : Closed Book, Closed Notes. (会发Eisberg量子物理课本封面後的常数表) 1. (a) What is the isotope effect, and how did this influence BCS theory? (b) Describe the crucial elements of BCS theory. (c) From typical T_C of order 10°K, infer typical Cooper pair size. (d) Derive magnetization M as a function of B/T for paramagnetism, plot the result, and interpret the physical limits of B/T → 0 and ∞. What is Curie's constant? 2. (a) Explain the transparency of a good salt crystal, and the "metallic shine" of metals. (b) Illustrate how the Krönig-Penney potential is a simplified model of a metal lattice. For lattice periodicity a, write down the Bloch solution. (c) Give the arguments from K-P potential for the formation of band structure. Draw rhe ω-k dispersion diagram up to the second Brillouin zone. (d) For an electron in a K-P type potential experiencing an external force, deduce the effective electron mass m*. Illustrate the k dependence in the first Brillouin zone. 3. (a) Sketch the Chadwick experiment and discuss how the neutron was inferred. (b) Sketch the Hofstadter experiment, compare the advance with respect to Rutherford scattering experiment, and discuss the principle used to infer nuclear strcture. (c) Sketch and interpret the effective charge density ρ(r) that emerged. Explain why ρ(0) drops with A. 4. (a) Draw the binding energy per nucleon vs atomic number A and give an explanation of the qualitative features and their origins. (b) Construct the energy levels of the shell model and predict the first 6 magic numbers. Give arguments fot splittings, and explain the meaning of magic numbers. (c) Explain the pairing interaction in nuclear physics, and its impact. (d) Predict the ground state spin and parity of 6(C)14, 7(N)15, 8(O)16, 8(O)17, 19(K)39, 19(K)40. --

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