Energy levels for the Hydrogen Atom

In summary, the conversation discusses the Schodinger and Dirac equations for the Hydrogen Atom and how they provide different eigenvalues for the spectrum. It is mentioned that Sommerfeld was the first to find the correct expression for the levels, using a combination of relativity, Schodinger equation, and other factors, but there is a question about whether there is a reference for this calculation. The speaker mentions solving the problem with the Dirac equation but is curious about how Sommerfeld reached a similar result, although he could not take into account the electron's spin. The conversation ends with a request for a reference on Sommerfeld's work, as it cannot be found online.
  • #1
ClubDogo
9
0
Hello everybody.
As you surely know, the Schodinger 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, schrodinger 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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  • #2
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.
 
  • #3
So?

Ok... but could you write down a reference?
I'm interested in seeing this thing.
 
  • #4
I haven't found anything on the internet. I'll look it up in some books.
 

1. How are the energy levels for the Hydrogen Atom determined?

The energy levels for the Hydrogen Atom are determined by solving the Schrödinger equation, which is a mathematical equation that describes the behavior of quantum particles. This equation takes into account the electron's mass, charge, and the attractive force between the electron and the proton in the nucleus.

2. What is the significance of the energy levels for the Hydrogen Atom?

The energy levels for the Hydrogen Atom are significant because they determine the possible states that the electron can occupy around the nucleus. These energy levels also correspond to the different wavelengths of light that are emitted or absorbed when the electron changes energy states, which is essential in understanding atomic spectra.

3. What is the relationship between the energy levels and the size of the Hydrogen Atom?

The energy levels for the Hydrogen Atom are inversely proportional to the size of the atom. This means that the higher the energy level, the larger the orbit of the electron around the nucleus. Conversely, the lower the energy level, the smaller the orbit of the electron.

4. Can the energy levels for the Hydrogen Atom be observed experimentally?

Yes, the energy levels for the Hydrogen Atom can be observed experimentally through spectroscopy. By passing light through a sample of hydrogen gas, scientists can observe the different wavelengths of light that are emitted or absorbed, corresponding to the energy levels of the electrons in the atom.

5. Do all atoms have the same energy levels as the Hydrogen Atom?

No, the energy levels for the Hydrogen Atom are unique because it has only one electron. Other atoms with multiple electrons have more complex energy level diagrams, as the electrons interact with each other and the nucleus in different ways.

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