Energy levels for the Hydrogen Atom

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Discussion Overview

The discussion centers on the energy levels of the Hydrogen atom, specifically comparing the results obtained from the Schrödinger equation and the Dirac equation. Participants explore the historical contributions of Sommerfeld and seek references for his approach to deriving energy levels.

Discussion Character

  • Exploratory, Historical, Debate/contested

Main Points Raised

  • One participant asserts that the Schrödinger treatment yields incorrect eigenvalues for the Hydrogen atom's spectrum, while the Dirac equation provides the correct values.
  • Another participant clarifies that Sommerfeld's results are not exactly the same as those from the Dirac equation, noting that Sommerfeld's approach did not account for electron spin and involved a relativistic theory of two charges in elliptical orbits.
  • A request for references regarding Sommerfeld's calculations is made, indicating an interest in understanding his methodology.
  • A participant mentions difficulty finding information online and expresses intent to search through books for relevant references.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the accuracy of Sommerfeld's results compared to the Dirac equation, and there is an ongoing search for references to clarify Sommerfeld's approach.

Contextual Notes

The discussion highlights the limitations of Sommerfeld's model, particularly its neglect of electron spin, and the dependence on historical context for understanding the evolution of quantum mechanics.

ClubDogo
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Hello everybody.
As you surely know, the Schrödinger treatment of the Hydrogen Atom gives wrong eigenvalues for the Spectrum. The Dirac equation provides for a correct one. On the other hand, the first who found the correct expression for the levels was "mighty" Sommerfeld using a mixture of relativity, Schrödinger equation and other stuff. The question is: is there any reference for the correct calculus done as Sommerfeld did?
I solved the problem with Dirac equation but I'm curious to notice how Sommerfeld reached the same result...

Thankz
 
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Not exactly the same result, a close one, he couldn't have taken account on the presence of spin for the electron, so he basically provided a relativistic theory of 2 charges attracting by means of a Coulomb electrostatic interaction and moving in closed elliptic orbits.
 
So?

Ok... but could you write down a reference?
I'm interested in seeing this thing.
 
I haven't found anything on the internet. I'll look it up in some books.
 

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