课程名称︰量子物理上 课程性质︰物理系必带 课程教师︰高涌泉 开课学院：理学院 开课系所︰物理学系 考试日期（年月日）︰2018/11/6 考试时限（分钟）：110分钟 是否需发放奖励金：是 （如未明确表示，则不予发放) 试题 : 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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