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）︰2008/5/14
考試時限（分鐘）：10:20~12:30 (130分鐘)
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
Closed Book, Closed Notes. (會發Eisberg量子物理課本封面後的常數表)
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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