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）︰97/11/26
考試時限（分鐘）：60
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1. Consider a particle moving on a ring.
(a) To ensure that the particle moves freely on the circumference of a ring,
how should we write down the Hamiltonian?
(b) Can we treat the motion of the particle as a one-dimension problem?
(c) What is the Schrodinger equation of the particle in terms of ψ?
[You can write down the equation directly]
(d) Write down a possible solution for the Schrodinger equation.
(e) Determine the normalized wavefunctions.
(f) What are the allowed energies for this system?
(g) Explain whether or not the uncertainty principle is violated when the
particle is in its ground state.
(h) Name a chemical compound for which the particle-in-a-ring can be used to
explain some of its electronic properties.
2. Consider non-degenerate case only, use bra-ket notation to prove the
following results:
(a) For a Hermitian operator, its eigenvalue must be real.
(b) The eigenkets of an operator are orthogonal if their corresponding
eigenvalues are different.
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