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課程名稱︰普通化學甲上
課程性質︰必修
課程教師︰林萬寅
開課學院：工學院
開課系所︰化學工程學系
考試日期（年月日）︰2011/11/09
考試時限（分鐘）：約15分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. The wave function for a particle of mass m confined in one dimensional box
of
length L is given by:Ψ(x)=√(2/L)×SIN(n pi x/L)
. Answer (B)-(G) for n = 4.
(A) Write the Schrödinger equation of the system within the box. 10%
(B) Sketch the probability density (y2) of finding the particle within the “
box” as a
function of x. 20%
(C) Give the positions of maximum probability. 20%
(D) Give the positions of nodes. 15%
(E) What is the probability of finding the particle within L/2 ￡ x ￡ 7L/8?
10%
(F) Write an expression for calculating the average position of the particle.
15%
(G) What is the average position of the particle? 10%
(Hint: answer (D) and (G) by inspection of the plot in (B) without
calculations)
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