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4604_ProblemSet5_fa07

# 4604_ProblemSet5_fa07 - PHY4604 Fall 2007 Problem Set 5 PHY...

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PHY4604 Fall 2007 Problem Set 5 Department of Physics Page 1 of 3 PHY 4604 Problem Set #5 Due Wednesday October 31, 2007 (in class) (Total Points = 130, Late homework = 50%) Reading: Griffiths Chapter 4 Sections 4.1, 4.2, and 4.3. Useful Math: ) / ( tan 16 1 ) ( 16 ) ( 24 ) ( 6 ) ( 1 5 2 2 4 2 2 2 2 3 2 2 4 2 2 2 a x a x a a x x a a x x a x dx x a x + + + + + + = + ) / ( tan 16 1 ) ( 16 ) ( 24 7 ) ( 6 ) ( 1 3 2 2 2 2 2 2 3 2 2 2 4 2 2 4 a x a x a a x x a x x a x a dx x a x + + + + + = + = 2 1 a a x e dx xe ax ax Problem 1 (20 points): Use separation of variables in Cartesian coordinates to solve the infinite cubical well (or “particle in a box”): + = 0 ) , , ( z y x V otherwise L z L y L x < < < < < < 0 , 0 , 0 (a) (10 points) Find the stationary states and the corresponding energies. (b) (5 points) Call the energies E 1 , E 2 , E 3 , …, in order of increasing energy. Find E 1 , E 2 , E 3 , E 4 , E 5 , and E 6 . Determine the degeneracies ( i.e. the number of different states with the same energy). (c) (5 points)

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4604_ProblemSet5_fa07 - PHY4604 Fall 2007 Problem Set 5 PHY...

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