課程名稱︰近代物理
課程性質︰系選修
課程教師︰林清富
開課學院：電機資訊學院
開課系所︰電機系
考試日期（年月日）︰2011/1/10
考試時限（分鐘）：3小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.A beam of electrons is incident with energy of 0.4eV,
the energy of potential barrier is 3.0 eV.The current of
incident side is measured as 1.00A.What is the magnitude of
current on the other side of barrier?(10%)
2.The potential energy is distributed as the following function:
V(x)=∞ as x＜0
V(x)=0.5kx^2 x≧0
What is the total energy that corresponding to each energy level?(10%)
3.There is a 3-Dimensional cubic box with the length of each side L.
The potential energy inside the box is zero, otherwise infinite large.
If the energy of ground state is called E1,what is the degeneracy
of E3? That is, the degeneracy of the second excited state?(10%)
4.(a) What is the angular momentum of the electrons of hydrogen atom
with quantum number l=1 and l=2? And their projection on the
z-axis? Please list all possibilities.(5)
(b) What is the corresponding projection angle?(5)
5.The potential energy of a particle is distributed as following:
V(r)=0 for r＜R
V(r)=Vo for r≧R
(a)What is the quantization of the angular momentum of the electrons
on the shells?(Hint:L=? or L^2=?)(10%)
(b)Please assign the quantum numbers of three electrons which are
in the ground state of the system.(10%)
6.Please calculate the position r of maximum possibility of occurence
of the electron n=2 l=0?(Hint: R20(r)=1/2√2*a0^-3/2*(2-r/a0)*exp(-r/2a0))
(10%)
7.The total atomic angular momentum is called J which corresponds to
index j=5/2.
(a)What are the possible values of index l?(5%)
(b)What is the angle between L and S for the largest l such that J=L+S?(5%)
8.Can the ground state of rotational energy level be occupied by
more than two electrons?Why?(6%)
9.Can the ground state of vibrational energy level be occupied by
more than two electrons?Why?(6%)
10.Please compare the difference of Fermions and Bosons.(8%)
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