Physics · Advanced university
Scattering, currents and probability conservation · revision notes
Scattering models compare incoming and outgoing waves far from a localized interaction. Boundary conditions identify which waves are physically incident.
Key ideas and conditions
Asymptotic waves
Scattering models compare incoming and outgoing waves far from a localized interaction. Boundary conditions identify which waves are physically incident.
Current
For a nonrelativistic one-dimensional wave, j=(ℏ/m) Im(ψ* ∂ψ/∂x). For a plane wave, current includes wave number as well as amplitude.
Transmission
Transmission probability is a transmitted-to-incident flux ratio. It is not always the squared transmission-amplitude ratio when wave numbers differ.
Conservation
For a real, time-independent nonabsorbing potential with the usual scattering channels, R+T=1. Absorption or additional channels require fuller accounting.
Explain without looking
- Explain why R+T=1 must not be imposed blindly on a model with absorption.
- For ψ=A exp(ikx), what determines the sign of current when mass is positive?
Further reading and review references
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