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）︰2018/11/6
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 :
Note: Using calculator is prohibited.
1.(a)(10%)How does H, the Hamiltonian operator, enter the Schrodinger equation
in quantum mechanics?
(b)(10%)The Hamiltonian operator H for a Spin 1/2 particle in an external m-
agnetic field |B> is of the form
H=-|μ_s>·|B>
What is |μ_s>? Explain your answer.
2.(a)(5%)Given that
8πhν^2 1
u(ν,T)=---------- ------------
c^3 e^(hν/kT)-1
What is u(ν,T), the Planck blackbody spectrum in terms of wavelength λ?
(b)(10%)Shows that λmax is proportional to 1/T (i.e., λmax=α/T) and iden-
tify the proportional constant α.
3.(a)(5%)What is the so-called Compton wavelength? How large is it?
(b)(10%)Can a free electron absorb a photon completely? Why?
4.(20%)Einstein argued that the blackbody (cavity) radiation "behaves as if it
consists of independent point-like energy quanta of magnitude hν" on the b-
asis of Wien's formula u(ν,T)=αν^3e^(-βν/T). What is the average energy
E(T) of the energy quantum?
5.(20%)Consider a particle of mass m in a (1-dimensional) box with infinite w-
alls :
0 , 0<X<a
V(x)={
∞, x<0,x>a
Use the Wilson-Sommerfeld quantization condition to obtain the energy levels
for this particle.
6.(10%)How did Sommerfeld "remove the degeneracy" in the Sommerfeld model of
the hydrogen atom?
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※ 編輯: TunaVentw (140.112.4.184), 11/06/2018 13:54:29
※ 編輯: TunaVentw (140.112.4.184), 11/06/2018 13:57:26