ps4 - Quantum Mechanics Problem Sheet 4(Individual help...

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

Unformatted text preview: Quantum Mechanics Problem Sheet 4 (Individual help with these problems is available in the workshop on Friday, 10 Feb 2006. Solutions should be handed in for marking at the start of the lecture on Tuesday, 14 Feb 2006.) 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 ( B e i kx + C e- i kx ) for x > , where E = ¯ h 2 k 2 / (2 m ) and k > 0. A , B , and C 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 , B , and C . For each of them, determine whether it is right- or left-moving. They represent the incident, reflected, and transmitted parts of the particle current. Which is which? (A little sketch with arrowsreflected, and transmitted parts of the particle current....
View Full Document

{[ snackBarMessage ]}

Page1 / 2

ps4 - Quantum Mechanics Problem Sheet 4(Individual help...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online