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）︰2019/01/10
考试时限（分钟）：120分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
Quantum Physics Final Exam
1.Consider the Hermition matrix M
1 i
M=( -i 1 )
(a)(5%)Find the eigenvalues of M.
(b)(10%)Find a diagonal matrix D and a unitary matrix U such that U^(-1)MU=D
2.(a)(15%)How did Born and Jordan arrive at the canonical commutation relation?
[p,q]=pq-qp=h/(2πi)I ?
(b)(10%)What is the so-called Heisenberg equation of motion for the dynamic-
al variable A in the matrix mechanics? (A'=?)
3.(10%)If a particle of mass m moves with a constant speed v, what is the
associated de Broglie wavelenght and frequency? (The answer should be
consistent with special relativity.)
4.(15%)Let J be the probability current obeying the equation
∂ρ