WeekProb_Nov16 - Discussion Problems Due in section for...

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Unformatted text preview: Discussion Problems Due in section for weeks of Nov 16, 2009 Problem 1 Tipler 6-54 7C staff April 19, 2006 Problem 1 Tipler 6-21 The wave functions of a particle in a one-dimensional infinite square well are given by, n ( x ) = 2 L sin nx L n = 1 , 2 , 3 , Show that for these functions n ( x ) m ( x ) dx = 0, i.e. , that n ( x ) and m ( x ) are orthogonal. Problem 2 Tipler 6-53 A particle of mass m is in an infinite square well potential given by, V = x <- 1 2 L V = 0- 1 2 L < x < + 1 2 L V = + 1 2 L < x Since this potential is symmetric about the origin, the probability density | ( x ) | 2 must also be symmetric. (a) Graph this potential. Show that this implies that either (- x ) = ( x ) or (- x ) =- ( x ). (b) Show that the proper solutions of the time-independent Schrodinger equation can be written ( x ) = 2 L cos nx L n = 1 , 3 , 5 , 7 , and ( x ) = 2 L sin nx L n = 2 , 4 , 6 , 8 , (c) Show that the allowed energies are the same as those for the infinite square well given by Equation 6-24.(c) Show that the allowed energies are the same as those for the infinite square well given by Equation 6-24....
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This note was uploaded on 02/19/2010 for the course PHYSICS 7C taught by Professor Lin during the Fall '08 term at University of California, Berkeley.

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