Lecture 24, 18.300, Tue May 3, 2022.
Topic: General first order scalar pde.  Bi-characteristics. Correspondence
 principle in QM. Eikonal equation and Rays.
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1- General Nonlinear First Order PDE.
   Derive and justify characteristic form. Bicharacteristics.
2- Example: Eikonal, write characteristics.
   For constant velocity show caustic formation.
   Ray tube collapse.
3- Eikonal: derive from wave equation. Geometrical optics anzatz.
   Motivate/justify.
4- Schrodinger equation: Classical limit. Derive equation for the
   phase [again Geometrical optics anzatz].
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