課程名稱︰量子力學二
課程性質︰必修
課程教師︰高涌泉
開課學院：理學院
開課系所︰物理所
考試日期（年月日）︰2014/06/19
考試時限（分鐘）：130
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.
a)What is the so-called bonding molecular orbital of the hydrogen molecule ion?
What is the anti-bonding molecular orbital?
1 3
b)Is the first excited state of helium S_0 or S_1? Why?
c)Is the total-spin state of the two electrons in the ground state for the
hydrogen molecule a spin-0 or a spin-1 state? Why?
2.Use the Born approximation to determine the differential cross section for
the potential energy
C
V = ───
r^2
where C is a constant, corresponding to a 1/r^3 force.
3.Calculate 〈n_{k,s}│E│n_{k,s}〉and〈n_{k,s}│E^2│n_{k,s}〉where E is the
electric field operator and │n_{k,s}〉is the state with n_{k,s} photons,
each with momentum hbar k and polarization s.
4.The Hamiltonian for a charge q in a 1-dimensional harmonic oscillator in a
classical time-dependent electric field is given by
H = H_0 + H_1
where
(p_x)^2 1 2 2
H_0 = ──── + ── mω x
2m 2
and
H_1 = -q x│E│exp(-t/τ).
Suppose that at t = 0 the oscillator is in the n = 0 ground state. Treat H_1
as a perturbation. Use the time-dependent perturbation theory to calculate
the probability to first order that the oscillator is in an excited state at
t = ∞.
5.Explain
a)The optical theorem.
b)The electric dipole transition.