課程名稱︰量子物理下 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）︰2019年4月18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 : 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? --

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