课程名称︰量子物理下
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）︰2019年4月18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 :
Quantum Physics Midterm Exam.
4/18/2019
1.(20%) Consider the delta function potential V=gδ(x) as shown in Fig.1. Par-
ticles with energy E>0 are incident from the left. What is the transimission
coefficient?
2.Consider the time-independent Schrodinger equation for hydrogen atom. We
know that the eigenfunction Ψ are formed by taking the product
Ψ_{n,l,ml}(r,θ,φ)=R_{n,l}(r)Θ_{l,ml}(θ)Φ_{ml}(φ)
(a)(5%)What is Φ_{ml}(φ)?
(b)(5%)Why must the quantum number ml be an integer?
(c)(10%)Given n, what are the possible values for l and ml?
3.(20%) A measurement of Sy for a spin 1/2 system leads to the eigenvalue
-hbar/2. Subsequently, a measurement of Sx cos(φ)+Sy sin(φ) is carried out
. What is the probability that the result is -hbar/2?
4.The spin-orbit interaction will break the degeneracy of the 2^2P_{3/2},
2^2P_{1/2}, 2^2S_{1/2} states of hydrogen atom.
(a)(10%) Which of the 3 states has the highest energy if only this interact-
ion is taken into account? Which has the lowest energy? Explain your ans-
wer.
(b)(10%) If we compare the energy associated with the spin-orbit interaction
with the energy of the ground state, what is the ratio? You only need to
give an order-of-magnitude estimate.
5.(a)(10%) What is the Aharonov-Bohm effect?
(b)(10%) What is the Schrodinger-Paulic equation?