課程名稱︰量子物理下
課程性質︰物理系大三必帶
課程教師︰高涌泉
開課學院：理學院
開課系所︰物理學系
考試日期（年月日）︰2019/06/18
考試時限（分鐘）：110分鐘
（如未明確表示，則不予發放）
試題 :
Quantum Physics Final Exam
6/18/2019
1.(a)(10%) What is the density operator (matrix) ρ that describes a complete-
ly polarized beam with S_x+? (in the S_z basis)
(b)(10%) What ρ describes an incoherent mixture of an S_x+ ensemble and
S_x- ensemble with equal weight? (in the S_z basis)
2.(a)(5%) What is the ground state of the helium atom in spectroscopic notati-
on?
(b)(15%) A schematic sketch of the lowest excited states of helium is given
by
E↑ ──── ^1P_1
│ ──── ^3P_2, ^3P_1, ^3P_0
│ ──── ^1S_0
│ ──── ^3S_1
Can you provide an explanation for the order of the levels?
3.(a)(5%) What is the so-called Dulong-Petit law?
(b)(5%) What is the so-called Debye T^3 las?
(c)(10%) One could derive (a) and (b) with the Debye model. Sketch the deri-
vation.
4.(a)(5%) Sketch the graph of specific heat versus temperature for the liquid
helium around T=2.18K.
(b)(5%) Sketch the graph of specific heat versus temperature for the ideal
Bose gas around the condensation temperature Tc.
5.(10%) Derive the average energy of an electron in a metal at zero temperatu-
re from the Fermi distribution (E_F= the Fermi energy).
6.(a)(10%) How is a superconductor different from a perfect conductor?
(b)(10%) What is the so-called Bloch's theorem?