# comp2 - Computer project 2 PHZ 5156 Results due Thursday,...

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Computer project 2 PHZ 5156 Results due Thursday, September 21 Please submit your code and plots wherever requested. Results can be handed in either as a hardcopy, or as an electronic document (e.g. tex, latex, MS word, or even a .pdf) sent via email. 1. A wave function in one dimension evolves according to the Schrodinger equation as, i ~ ∂ψ ( x, t ) ∂t = ± - ~ 2 2 m 2 ∂x 2 + V ( x ) ² ψ ( x, t ) Show that if V ( x ) = 0 for a t = 0 wave packet given by ψ ( x, t = 0) = 1 σ 0 π e ik 0 x e - ( x - x 0 ) 2 / 2 σ 2 0 that the analytic expression for the time evolution is given by ψ ( x, t ) = 1 σ 0 π e ik 0 ( x - st/ 2) e - ( x - x 0 - st ) 2 / 2 σ 0 σ with s = ~ k 0 /m and σ = σ 0 + i ~ t 0 . 2. Implement the Crank-Nicholson scheme to calculate the quantum-mechanical time evolution of a one-dimensional Gaussian wave packet with hard wall boundaries, so that the wave function vanishes at x = 0 and x = l . For the evolution, use the deﬁnitions, x j = ( j + 1) h t n = n Δ t ψ j n = ψ ( x

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## This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.

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comp2 - Computer project 2 PHZ 5156 Results due Thursday,...

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