[試題] 105-1 高涌泉 量子物理上 期中考
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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