課程名稱︰量子物理下
課程性質︰必修
課程教師︰高涌泉
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2018/6/26
考試時限（分鐘）：110
試題 :
1 (10pt+5pt)
Consider the density operator ρ=(|z,+><z,-| + |x,-><x,-|)/2 :
(a) What is the matrix representation of ρin the S_z basis?
(b) What is <S_x> for the state described by this ρ?
2 (10pt)
It is stated in the textbook(Eisberg) that an experimental fact provided the primary evidence that led Pauli to the discovery of the exclusion principle. What is this experimental fact?
3 (10pt+10pt)
(a) One can estimate the critical temperature T_c for the Bose-Einstein condensation by equating the thermal de Broglie wavelength with the mean interparticle distance. What is this approximate T_c in terms of m, N, V, h, and k?
(m: mass of particle, N: number of particle, V: volume of the system, h: Planck constant, k: Boltzmann constant)
(b) What is the so-called λtransition in liquid helium?
4 (10pt+10pt)
Consider the free electron gas at zero temperature.
(a) What is the Fermi energy E_F in terms of m, N, V, h?
(m: mass of electron, N: number of electron, V: volume of the system, h: Planck constant)
(b) What is the average energy of an electron E in terms of E_F?
5 (10pt+10pt)
(a) What is the so-called London equation?
(b) How did Fritz and Heinz London use this equation to explain the Meissner effect?
6 (10pt+10pt)
Explain the following terms
(a) Aharonov-Bohm effect
(b) energy bands