課程名稱︰普通物理學甲下 課程性質︰必帶 課程教師︰林敏聰教授 開課學院：工學院 開課系所︰材料系 考試日期（年月日）︰101.6.16 考試時限（分鐘）：09:00 ~ 14:00 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. Please prove that the electromagnetic wave is propagating with the speed of light by using the Maxwell's equations in vacuum and the wave equation. (10%) 2.The figure below shows four wire loops, with edge lengths of either L or 2L. All four loops will move through a region of uniform magnetic field B (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the emf induced as they move through the field, greatest first. Explain how do you make such a claim? (10%) ┌───────┐ │‧ ‧ ‧ ‧ ‧│ ┌──┐ ┌────┐ ┌────┐ ┌──┐ │ │B │ │ │ │ │ │ │ │ │‧ ‧ ‧ ‧ ‧│ │ │ │ │ │ │ │ │ │ │ └──┘ └────┘ │ │ │ │ │‧ ‧ ‧ ‧ ‧│ a b │ │ │ │ │ │ └────┘ └──┘ │‧ ‧ ‧ ‧ ‧│ c d └───────┘ 3.Consider an arbitrary charge distribution ρ(r) within a volume V. Please express the electric potential Φ(r) with terms of monopole charge, dipole moment, and quadrupole moment.(Hints: using binomial expansion.) (15%) 4.Explain the concept of duality, and give one example of experiment (described in details, please) for the "wave" behaving as "particle" and "particle" as "wave", respectively. (10%) 5.The potential energy of a simple harmonic oscillator is given by U = (1/2)mω^2x^2. Let Ψ = Ae^(-Bx^2) be a solution of the Schrödinger wave equation. What are B and the energy of the state? (10%) 6.Please write down the operator of linear momentum P in the one-dimensional Schrödinger equation. Please try to give a "heuristic derivation" of this operator. (10%) 7.(a) Consider a one-dimensional potential well with infinite height and width of d for a particle of energy E. (We call the solution of wave function and energy eigenfunction and eigenenergy, respectively.) The minimal energy of the particle existing in this quantum well is called ground state. Please estimate the minimal temperature for exciting the particle to the next higher energy state. (15%) (b) Give a brief interpretation of your solution with comparison of classic physics. (5%) 8.Design an experiment to prove that it is the movement of electrons but not positive charged ions caused the electric current flow in a metallic conductor. (10%) 9.In scanning tunneling microscopy (STM) experiments, the tunneling behavior can be simplified as an one-dimensional (along z direction) metal-vacuum- -metal tunneling junction (see figures). (a) Please find the transmission coefficient T, from sample to tip. (7%) (b) Please show that the transmission coefficient is proportional to e^(-2ρs) _ when ρs >> 1, ρ = √(2m(U－E)/h^2). (8%) Good luck and Have a nice summer vacation!!!(Total 110%) 註：h頭上有條底線，代表h-bar。 --

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