# ps09 - Homework(9 for Physics 316 Modern Physics...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.

Ask a homework question - tutors are online