課程名稱︰普通物理學甲下
課程性質︰系定必修
課程教師︰林敏聰
開課系所︰電機系
考試時間︰6/19 2005 0900~1300 (視情況延長)
試題 :
1. (a) What is the relation between 向量E, 向量B, and the velocity 向量v
of the electromagnetic wave? (5%)
(b) Please derive the relation of c = (με) ^ (-1/2) and E/B = c in a
0 0
traveling electromagnetic save in application of Maxwell's equations.
(10%)
2. Please derive the kinetic energy K and the E=mc^2 relation in special
relativity with interpretation. (10%)
3. (a) If the kinetic energy K and the momentum p of a particle can be
measured, it should be possible to find its mass m and thus identify
the particle. Show that (pc)^2 - K^2
m = ----------------
2Kc^2
(5%)
(b) Show that this expression reduces to an expected result as u/c --> 0,
in which the u is the speed of the particle.
4. Explain the concept of duality, and give two examples (described in
details, please) for the "wave" behaving as a "particle" and "particle"
as "wave", respectively. (15%)
5. Consider an electron tunneling through a barrier, having barrier height
3eV and a width 1 nm. What is the tunneling probability of this electron
if it has initial energy of 1eV? (Please derive the equation you may need
from Schroedinger equation.) (15%)
Φ = 3eV
________
E = 1eV | |
. ---------->| |
| |
--------------------------------------
6. Please use the Bragg relation in a low energy electron diffraction
experiment to express the vertical interlayer distance d by the primary
energy of the electron Ep, electron mass m, and the incident angle θ with
respect the sample surface. (10%)
7. Please write down the Schroedinger equation with a one-dimensional
potential well with height V and width d for a particle with energy E, and
find out the solution of the wave function. Give a brief interpretation of
your solution. (15%)
8. What is the Stern-Gerlach experiment? Please give the interpretation of
this experiment. (10%)
9. Good luck and have a nice summer vacation!!! (Total 100%)
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