課程名稱︰物理化學二
課程性質︰必帶
課程教師︰陳振中
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰97/10/24
考試時限（分鐘）：120
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1. The Balmer series has an equatiom of the following term:
1 1 1
─ = R [── - ──]
λ 2^2 n^2
The energy expression of the Bohr's model of an one-electron atom:
Z^2
En = -2.178*(10^-18) ──
n^2
(a) Derive the value of R in terms of the Planck constant and light velocity.
(b) What is the shortest wavelength of the emission spectrum of Be(3+)?
^ ^ ^ ^
2. Evaluate the commutators [x, Px] and [y, Px].
3. The wavefunctions for a quantum mechanical harmonic oscillator are given as
follow:
In general the wavefunctions for the harmonic oscillator are given by:
Ψn = Nn*Hn*((α^0.5)x)*exp(-0.5*α*(x^2))
where α = ((k*μ)^0.5)*(2π)/h
1
Nn = ───────*(α/π)^0.25
((2^n)*n!)^0.5
Hn are the Hermite polynomials.
Based on the above information, determine the wavefunctions of the
following system:
1
V(x) = ─k(x^2) for x≧0, V(x) = ∞ for x＜0
2
4. Consider a particle in a one-dimension well
P.E.
∞↑
│
V┤ ┌───
│ │
│ │
0└─────┘
├──→x
←────→
L
(a) What is the Hamiltonian for the region of 0≦x≦L? Without considering any
boundary condition, write down the eigenfunctions of the Hamiltonian.
(b) What is the Hamiltonian for the region of x＞L? Assume that the total
energy of the particle is less than V, write down the eigenfunctions of
the Hamiltonian without considering any boundary condition.
(c) Impose proper boundary conditions and explain whether the energy levels
are quantized or not.
[Hints: the wavefunctions must be smooth at x=L]
(d) Explain whether E=0 is an allowed energy value or not.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.243.38
※ 編輯: blackpanther 來自: 140.112.243.38 (01/22 22:56)