How make a confront between energy levels?

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SUMMARY

The discussion centers on the discrepancies in energy levels predicted by the Schrödinger Equation and the Relativistic Schrödinger Equation for the Hydrogen Atom, highlighting that the Dirac Equation provides the correct calculations. Arnold Sommerfeld's work, which combines Special Relativity with the Schrödinger Equation, reportedly yields results consistent with the Dirac Equation for hydrogen-like atoms. The participants express a desire to locate Sommerfeld's calculations, indicating a gap in accessible resources on this topic.

PREREQUISITES
  • Understanding of the Schrödinger Equation and its limitations
  • Familiarity with the Dirac Equation and its applications
  • Knowledge of Special Relativity principles
  • Basic concepts of quantum mechanics and atomic structure
NEXT STEPS
  • Research Arnold Sommerfeld's contributions to quantum mechanics
  • Explore the derivation and implications of the Dirac Equation
  • Investigate the historical context and limitations of the Relativistic Schrödinger Equation
  • Study the relationship between Special Relativity and quantum mechanics in atomic physics
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Physicists, students of quantum mechanics, and researchers interested in atomic theory and the historical development of quantum equations.

ClubDogo
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Hi there.
It is a fact that, historically, the Schrödinger Equation provides wrong energy levels for the Hydrogen Atom. The same is for The Relativistic Schrödinger Equation (hehe, this is not known by most of students, seek it in arxiv database, it was the original developed by Schrödinger that was totally relativistic, but in a second development the relativistic invariance was broken indeed for the reasons involving the inappropriate descriptionof energy levels, and Klein Gordon.
So the correct calcucus come with the Dirac Equation.
But... there is a fact.
The GREAT Arnold Sommerfeld did some high technical calculus with:
1) Special Relativity
2) Schrödinger Equation
... and come to THE SAME RESULTS OF DIRAC EQUATION FOR AN HYDROGENOIS ATOM!

I am desperately seeking for this calculations but i cannot find them anywhere, in books, in the web...
Can anyone help me?

Thankz
 
Physics news on Phys.org
Well, I don't know what he did. I'm curious myself now! hehe :)
but are you sure he used Schrödinger equation? because as I see, it would be create a controversy: on one side you're using relativity, and on the other side you're using a classical energy equation (through Schrödinger equation)
 

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