Sokhotski–Plemelj Boundary Jump
Discover how approaching a Cauchy singularity from opposite sides creates an imaginary jump.
Free theory articleDiscover how approaching a Cauchy singularity from opposite sides creates an imaginary jump.
Concept & interpretation
The Sokhotski–Plemelj theorem connects the boundary values of analytic functions integrated over a real line to the Cauchy principal value and a singular jump term. When approaching a Cauchy singularity from opposite sides of the real axis, the imaginary component exhibits a discrete jump, proportional to the delta function.
Experiment
Using the interactive module Sokhotski-Plemelj Boundary Jump:
- Select the Probe position along the real axis.
- Select a value for the Width regularizer parameter.
- Select the Approach side.
- Observe the Real part and Imaginary part outputs, as well as the Imaginary boundary limit.