課程名稱︰量子物理上
課程性質︰物理系必帶
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）︰2018年1月4日
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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)
-----│-----E(=2Vo)
│
V0 │──
──────
0 x
--
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