# Ps1 - Quantum Mechanics Problem Sheet 1(These problems will be discussed in the practice session on Friday 20 Jan 2006 1 Which of the following

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Quantum Mechanics Problem Sheet 1 (These problems will be discussed in the practice session on Friday, 20 Jan 2006) 1. Which of the following functions make good wave functions for describing a particle moving in one dimen- sion? Sketch the probability density for each of them and check whether it is normalizable. Determine the normalization constant C n for those that are normalizable. (The parameters λ n are all real and positive.) (a) ψ 1 ( x ) = 0 for x < 0 , C 1 sin( λ 1 x ) for 0 x 2 π/λ 1 , 0 for x > 2 π/λ 1 . (b) ψ 2 ( x ) = C 2 1 x + λ 2 for all x . (c) ψ 3 ( x ) = C 3 exp( λ 3 x 2 ) for all x . (d) ψ 4 ( x ) = C 4 exp( - λ 4 | x | ) for all x . 2. The wave function of a particle moving in one dimension is given by: ψ ( x ) = ± B exp( βx ) for x < 0 B exp( - 2 βx ) for x 0 , where β is a real and positive constant. (a) What is the probability density for Fnding the particle along the x axis? Sketch this function. (b) Calculate the normalization constant

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## This note was uploaded on 04/07/2008 for the course PHYS F3026 taught by Professor Eberlein during the Spring '06 term at Uni. Sussex.

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Ps1 - Quantum Mechanics Problem Sheet 1(These problems will be discussed in the practice session on Friday 20 Jan 2006 1 Which of the following

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