[試題] 105-2 高涌泉 量子物理下 期中考
課程名稱︰量子物理下
課程性質︰必修
課程教師︰高涌泉
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰106.4.20
考試時限（分鐘）：180
試題 :
Quantum Physics Midterm Exam 4/20/2017
(20%)
1. Suppose a spin -1/2 particle is in the state x = 1/sqar(6) (1-i; 2). What
are the probabilities of getting h_bar/2 and -h_bar/2 if you measure (a)S_x
and (b) S_y?
(20%)
2. The spin-orbit interaction energy (Hamiltonian) for the hydrogen atom is of
the form H_SO = A (SL) / (4πε_0r^3), where A is a constant.
(a) What is A? Show your derivation.
(b) This interaction will break the degeneracy of ^2P_(3/2), ^2P_(1/2),
^2S_(1/2). Which of the 3 states has the highest energy if only H_SO
is taken into account besides the Coulamb interaction? Which has the
lowest energy?
(20%)
3. (a) What is the Zeeman effect?
(b) What is the anomalous Zeeman effect?
(15%)
4. Write down the normalized anti-symmetric total eigenfunction for a system
of 3 particles, in which the interaction between the particles are ignored.
(15%)
5. One of the famous Hund's rules says that, other things being equal, the
states of highest spin will have the lowest energy. How can this rule be
explained in quantum mechanics?
(10%)
6. It is will known that Bohr and Einstein have different views about quantum
mechanics. How are their views different?
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