Unformatted text preview: Homework (9) for Physics 316, Modern Physics I (Hoffstaetter/Drasco/Thibault) Due Date: Friday, 04/08/05  9:55 in 132 Rockefeller Hall Exercise 1: In Electrodynamics the charge density ρ ( ~x, t ) and the current density ~ j ( ~x, t ) satisfy a con tinuity equation, ∂ ∂t ρ ( ~x, t ) + ~ ∇ · ~ j ( ~x, t ) = 0 . (1) Show that the probability density ρ =  Ψ( ~x, t )  2 satisfies the same continuity equation together with the probability current density ~ j = ¯ h m Im { Ψ( ~x, t ) * ~ ∇ Ψ( ~x, t ) } . Exercise 2: Given a wave function Ψ( x, t ) at t = 0 as (a) Ψ( x, 0) = A a e x 2 2 σ and (b) Ψ( x, 0) = A b e β  x  , where A a and A b are chosen in each case to normalize the wave function to 1. For each case, find the momentum representation of the wave function, i.e. find F ( k ) so that Ψ( x, t ) can be written as Ψ( x, t ) = Z ∞∞ F ( k ) e i [ kx ω ( k ) t ] √ 2 π dk . (2) Exercise 3: Given a wave function Ψ( x, t ) at t = 0 as Ψ( x, 0) = A a e...
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.
 Spring '05
 HOFFSTAETTER
 Physics, Charge, Current, Work

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