This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Quantum Mechanics Problem Sheet 4 (Solutions are to be handed in for marking before the lecture on Monday, 14 Feb 2005) 1. A stream of particles is scattered by an obstacle located at x = 0. The wave function describing the particles is Ψ( x, t ) = A e i Et/ ¯ h e i kx for x < , e i Et/ ¯ h ( C e i kx + D e i kx ) for x > , where E = ¯ h 2 k 2 / (2 m ) and k > 0. A , C , and D are constant complex coefficients. (a) Calculate the probability density ρ ( x, t ) for x < 0. (b) Calculate the probability current density j ( x, t ) for x < 0. (c) Calculate the probability density ρ ( x, t ) for x > 0. (d) Calculate the probability current density j ( x, t ) for x > 0. (e) The wave function given above is the sum of three distinct parts, labelled by the coefficients A , C , and D . For each of them, determine whether it is right or leftmoving. They represent the incident, reflected, and transmitted parts of the particle current. Which is which? (A little sketch with arrows labelled...
View
Full
Document
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

Click to edit the document details