Review_Midterm2

# Review_Midterm2 - University of Colorado, Department of...

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University of Colorado, Department of Physics PHYS3220, Fall 09, Some review problems - will not be graded - 1. The state of a particle in an inﬁnite square well with V ( x ) = 0 for 0 < x < a and V ( x ) = elsewhere is given by the wave function Ψ( x,t = 0) = ( q 30 a 5 x ( a - x ) , 0 x a 0 , else The wave function Ψ( x,t = 0) can be expanded in terms of a superposition of the stationary states of the inﬁnite square well as: Ψ( x,t = 0) = r 2 a X n =1 c n sin nπx a · Which c n do you expect has the largest magnitude? Explain brieﬂy. Then determine the n th coeﬃcient of the expansion. 2. The state of a particle in an inﬁnite square well is given by the wave function: Ψ( x,t = 0) = A ( χ 1 ( x ) + exp( ) χ 2 ( x )) where χ n ( x ) ( n = 1 , 2) are the two lowest stationary states of the inﬁnite square well. a) Find Ψ( x,t ), | Ψ( x,t ) | 2 , and < x > . Study the special cases φ = 0, φ = π/ 2 and φ = π . b) At time

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## This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.

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Review_Midterm2 - University of Colorado, Department of...

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