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Unformatted text preview: Discussion Problems Due in section for weeks of Nov 16, 2009 Problem 1 Tipler 654 7C staff April 19, 2006 Problem 1 Tipler 621 The wave functions of a particle in a onedimensional 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 653 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 timeindependent 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 624.(c) Show that the allowed energies are the same as those for the infinite square well given by Equation 624....
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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.
 Fall '08
 LIN
 Physics

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