课程名称︰量子物理上
课程性质︰物理系必带
课程教师︰高涌泉
开课学院：理学院
开课系所︰物理学系
考试日期（年月日）︰2018年1月4日
考试时限（分钟）：110分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
Qunatum Physics Final Exam
1/4/2018
1.(20%)Prove the following statement given in the 3-man (Born-Heisenberg-
Jordan) paper: If f(p,q) is any function of p and q, then
fq-qf=∂f/∂p(h/2πi) , pf-fp=∂f/∂q(h/2πi)
2.(10%)Explain fow Davisson and Germer show experimentally the wave nature of
matter.
3.(10%)
(a)What is the so-called Klein-Gorden (K-G) equation?
(b)What kinds of particles are described by the K-G equation? Give an
example.
4.(10%)
(a)According to Bloch, which scientist suggested to Schrodinger to search
for the wave equation for the de Broglie wave?
(b)When Bloch said to Heisenberg that "space was simply the field of linear
operations", what was Heisenberg's reply?
5.(15%)Consider a particle of mass m that can move freely along the x axis
anywhere from x=-a/2 to x=a/2, but which is strictly prohibited from being
found outside this region. What is the expectation value of p2 for the part-
icle in the ground state?
6.(10%)Sketch the approximate shape of the ground state wave function Ψ(x)
for the double delta function attractive potential in 1 dim.
(V(x)=-hbar^2λ/(2ma)(δ(x-a)+δ(x+a))
7.(15%)Given the wave function Ψ(x,t) in the position representation, what is
the wave function Ψ(p,t) in the momentum representation? (Consider the 3
dimensional case)
8.(20%)Consider the step potential V(x)={V0 ,x≧0 (V0>0). If a particle of
0 ,x<0
mass m moves with energy E=2V0 toward the origin x=0 from the left,
(a)What is the transimission coefficient T as defined in the class?
(b)What is the reflection coefficient R?
V(x)