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Unformatted text preview: Ben Sauerwine Practice for Qualifying Exams Problem Source: CMU Qualifying Exam August 2002 This problem considers electrons confined to a box of length a with a square well potential ( ) { } ⎩ ⎨ ⎧ ∞ ≤ ≤ = otherwise a x x V In addition to the confining potential, a strong magnetic field ensures that all electrons have parallel spins. Neglect interactions between electrons. (a) Write down the complete set of singleparticle wave functions ( ) x n ψ , properly normalized, and give their energies. These are the wellknown solutions to the particle in the box problem: ( ) 2 2 2 2 2 sin 2 a n m E x a n a x n n π π ψ h = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = (b) Write down the properly normalized twoelectron ground state wave function ( 2 1 , x x ) ψ in terms of the singleelectron wave functions ( ) x n ψ , and give its energy. The antisymmetric combination of these two wave functions (assuming both electrons are forced to be in the down state) is ( ) ( ) ( ) ( ) ( ) [ ] − − − =...
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This note was uploaded on 04/07/2012 for the course PHYSICS 767 taught by Professor Dr.jaouni during the Spring '12 term at Abu Dhabi University.
 Spring '12
 Dr.Jaouni

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