I How Fermat's principle interprets diffraction and interference

[zhouhao]

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1. Homework Statement
I have read several chapters of De Brogile's article "the theory of quanta".The motion of a particle could be analogious to a ray in general optics.This is an analogy between Maupertui's principle and fermat's principle.
How to use this theory to derive Schordinger equation?
How to explain the electron diffraction through fermat's principle?

Homework Equations

No equations.

The Attempt at a Solution

No ideas sorry

 

[azntoon]

.To derive the Schordinger equation, we can use the analogy between Maupertuis' principle and Fermat's principle. Maupertuis' principle states that a particle will move in such a way that its action (kinetic energy minus potential energy) is minimized. This can be applied to wave motion by noting that the action of a wave is proportional to its wavelength. Thus, in order for a wave to minimize its action, it must travel along the path of least time, which is exactly what Fermat's principle states. By applying this principle to wave motion, we can derive the Schordinger equation, which describes the evolution of a quantum system over time.To explain electron diffraction through Fermat's principle, we can note that when electrons interact with a crystal lattice, they behave as if they are waves. This is because the electrons in a crystal lattice are bound together by electrostatic forces, which cause them to vibrate in unison. This creates an interference pattern, which can be described by Fermat's principle. Fermat's principle states that a light ray will travel from point A to point B in the shortest possible time. Therefore, when electrons are diffracted through a crystal lattice, they take the path that minimizes their time, creating an interference pattern.