Schrödinger's equation, its derivation

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SUMMARY

Schrödinger's equation, as articulated by Richard Feynman, is fundamentally a product of Schrödinger's intuition rather than a derivation from existing theories. Unlike empirical formulas such as the Balmer or Rydberg equations, Schrödinger's equation does not stem from observational data but rather represents a conceptual leap in quantum mechanics. The discussion raises the possibility that future theoretical advancements may provide deeper insights into the origins and implications of Schrödinger's equation, akin to the developments following Bohr's work on the Balmer formula.

PREREQUISITES
  • Understanding of quantum mechanics fundamentals
  • Familiarity with Schrödinger's contributions to physics
  • Knowledge of empirical formulas in physics, such as the Balmer and Rydberg equations
  • Basic grasp of theoretical versus empirical approaches in scientific research
NEXT STEPS
  • Explore the derivation and implications of Schrödinger's equation in quantum mechanics
  • Study the historical context and significance of the Balmer and Rydberg equations
  • Investigate the philosophical implications of empirical versus theoretical frameworks in physics
  • Research advancements in quantum theory that may elucidate the foundations of Schrödinger's equation
USEFUL FOR

Physicists, students of quantum mechanics, and researchers interested in the foundational theories of modern physics will benefit from this discussion.

robertjford80
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Richard Feynman said:

Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger.

So does this mean that it is a equation like the Balmer formula or the Rydberg equation? There's no theory behind it, it's just an empirical formula? Did S just look at data and come up with an equation that fit the data? Is it possible that we will find out why the S equation is the way it is in the future, just as Bohr found out why the Balmer formula is the way it is?
 
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