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）︰2017年11月9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
11/9/2017
1.(10%)Show that the Wien's (displacement) law implies the Stefan-Boltzmann
law.
2.(15%)Derive the Rayleigh-Jeans law.
3.(15%)Let N be the number of photons in a box of volume V at temperature T.
N can be expressed as
kb T 3
N=αV(───)
c h
in which α is a dimensionless constant. What is α?(You do not have to
evaluate the integral that may appear in α.
4.(10%)Both Planck and Millikan did not like Einstein's idea of light quanta.
Why?
5.(15%)How did Eistein derive the Planck's blackbody radiation formula with
his A and B coefficients?
6.(20%)(a)Use the wilson-sommerfeld quantization method to obtain the energy
levels of a 1-dimensional simple harmonic oscillator (SHO).(The hamil-
tonian H is Px^2/2m + 1/2mω^2x^2.)
(b)Did Heisenberg obtain the same result for the same SHO using his new
quantum method?
7.(15%)Hesisenberg said in his ground breaking paper of 1925 that the classic-
al (1-dimensional) trajectory x(t) should be replaced by a set of quantities
of the form
{a(n,n-α)e^(iω(n,n-α)t}
in the quantum case. Now suppose that x^3(t) is represented by
{c(n,n-γ)e^(iω(n,n-γ)t}
in the quantum case. What is c(n,n-γ) in terms of a(n,n-α)?
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