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Unformatted text preview: Quantum Mechanics Problem Sheet 3 (Solutions are to be handed in for marking before the lecture on Monday, 7 Feb 2005) 1. Consider a particle that is confined in a onedimensional box, ie in a potential V ( x ) = for 0 ≤ x ≤ L ∞ for x < 0 and x > L . The particle is initially distributed uniformly inside the box, so that its wave function at time t = 0 is ψ ( x, 0) = N for 0 ≤ x ≤ L for x < 0 and x > L . (a) Determine the normalization constant N . (b) Write the initial wave function as a superposition of the stationary states φ n ( x ) in the box, ψ ( x, 0) = ∞ X n =1 c n φ n ( x ) , and calculate the expansion coefficients c n . Check your result by sketching ψ ( x, 0), φ 1 ( x ) , and φ 2 ( x ) and considering the symmetry of these functions around the middle of the box. (If you have understood how one gets the stationary states φ n ( x ) , you don’t need to rederive them — just quote the result from your lecture notes or from the previous problem sheet.) (c) Use the result of (b) to determine the timedependent wave function...
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This note was uploaded on 08/12/2008 for the course PHYS 252 taught by Professor Pocanic during the Spring '02 term at UVA.
 Spring '02
 POCANIC
 Physics, mechanics

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