On the origins of the Schrodinger equation

[5mrkv]

L'articolo da physorg più l'abstract dell'articolo originario.

Abstract

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave.
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Riporto un pezzo physorg:

In the case of quantum mechanics, there are so many convincing experimental results that many of the major textbooks do not really motivate the subject [of the Schrödinger equation's origins]. Instead, they often simply postulate the classical-to-quantum rules….The reason given is that 'it works.'" Coauthor Marlan O. Scully, a physics professor at Texas A&M University, explains how physicists may use the Schrödinger equation throughout their careers, but many still lack a deeper understanding of the equation. "Many physicists, maybe even most physicists, do not even think about the origins of the Schrödinger equation in the same sense that Schrödinger did," Scully told Phys.org. "We are often taught (see, for example, the classic book by Leonard Schiff, 'Quantum Mechanics') that energy is to be replaced by a time derivative and that momentum is to be replaced by a spatial derivative. And if you put this into a Hamiltonian for the classical dynamics of particles, you get the Schrödinger equation. It's too bad that we don't spend more time motivating and teaching a little bit of history to our students; but we don't and, as a consequence, many students don't know about the origins."

Aggiungo: Where did we get that [Schrödinger's equation] from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger. - The Feynman Lectures on Physics

La cultura in MQ consiste del corso di Istituzione di Fisica Teorica (MQ I,II). Personalmente mi sono trovato a disagio con i postulati della meccanica quantistica. L'unico analogo in meccanica classica che conosco e a cui posso fare riferimento è il principio di minima azione. Mi sono promesso di approfondire i postulati una volta posseduta una base migliore e mi fa piacere che qualcuno provi a smentire questa uscita di Feynman.

[VINX89]

Secondo me il Sakurai ("Modern Quantum Mechanics") fa una buona introduzione all'equazione di Schrodinger.
Ovviamente non segue le vicende storiche, però, utilizzando il formalismo operatoriale di Heisenberg e Dirac, giustifica ogni affermazione in modo elegante e convincente.