課程名稱︰量子物理上 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）︰107.11.10 考試時限（分鐘）：180 試題 : Quantum Physics Midterm Exam 11/10/2016 (10%) 1. Plot in a qualitatively correct way the following 3 blackbody radiation specturm (i.e., show in a graph the energy density u(v,T) as a function of v for a certain non-zero temperature): 1) Planck specturm, 2) Wien specturm, 3) Rayleigh-Jeans specturm. Put the 3 curves together in a single diagram. (10%) 2. (a) What is Wien's displacement law? (10%) (b) Express the Stephan-Boltzmann constant σ as a function of k, c and h. inf x^3 dx π^4 (you may use int ---------- = ------) 0 e^x - 1 15 (20%) 3. Einstein employed the notion of entropy to suggest the existence of light quantum. Explain Einstein's reasoning. (10%) 4. (a) Consider Bohr's model for hydrogen atom. What is the relation between the energy En and the orbital frequency vn. (n refers to the quantum number.) (10%) (b) How is Bohr's correspondence principle applicable to hydrogen atom? (15%) 5. Explain how Heisenberg recognized that x(t)y(t) is not necessarily equal to y(t)x(t) in his 1925 July paper (one-man paper). (15%) 6. Explain how Max Born derived the relation (px-xp)_nn = h / (2πi) from Heisberg's quantization condition inf 2 2 h = 4πm Σ [|a(n+α, n)| w(n+α, n) - |a(n, n-α)| w(n, n-α)] 0 -- 在很久的以後 你是否記得我 --

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