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）︰2018/04/24
考試時限（分鐘）：110
試題 :
1a (10%)
What is the so-called path integral representation of the 1-dimensional kernel K(x_f,t_f;x_i,t_i) defined by
K(x_f,t_f;x_i,t_i)=<x_f|exp(-iH(t_f-t_i)/(h-bar))|x_i> ?
1b (15%)
If you are asked to derive the answer to 1(a), how would you proceed?
1c(5%)
What is the Schrodinger equation for a particle with charge q and mass m in an electromagnetic field?
2(10%)
If you are asked to prove the relation [L_x,L_y]=ihL_z/2π,how would you proceed?
3(15%)
Describe how Stern and Gerlach obtained experimental evidence for the quantization of angular momentum in 1922?
4(15%)
A measurement of S_y for a spin 1/2 system leads to the eigenvalue +(h-bar)/2. Subsequently, a measurement of S_x*cosφ+S_y*sinφ is carried out. What is the probability of getting result +(h-bar)/2?
5a(15%)
What is the so-called fine structure of the hydrogen energy levels? Give a specific example.
5b(15%)
If you are asked to explain the fine structure quantatively, how would you proceed?
5c(5%)
What is the so-called Lamb shift?