How make a confront between energy levels?

In summary, the conversation discusses the historical inaccuracy of the Schrodinger Equation and the Relativistic Schrodinger Equation in providing energy levels for the Hydrogen Atom. The Dirac Equation is mentioned as the correct calculation for this. However, it is revealed that Arnold Sommerfeld was able to achieve the same results using a combination of Special Relativity and the Schrodinger Equation, which creates a controversy. The person speaking is seeking for Sommerfeld's calculations but has been unable to find them.
  • #1
ClubDogo
9
0
Hi there.
It is a fact that, historically, the Schrodinger Equation provides wrong energy levels for the Hydrogen Atom. The same is for The Relativistic Schrodinger Equation (hehe, this is not known by most of students, seek it in arxiv database, it was the original developed by Schrodinger 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) Schrodinger 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
 
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  • #2
Well, I don't know what he did. I'm curious myself now! hehe :)
but are you sure he used Schrodinger 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 Schrodinger equation)
 
  • #3


I can provide some insight into this topic. The Schrodinger Equation and the Relativistic Schrodinger Equation were developed to describe the behavior of particles at the atomic level. However, as you mentioned, these equations were found to provide incorrect energy levels for the Hydrogen Atom. This led to the development of the Dirac Equation, which is a more accurate description of energy levels for this system.

It is interesting to note that Arnold Sommerfeld was able to obtain the same results as the Dirac Equation using a combination of Special Relativity and the Schrodinger Equation. This is a testament to his mathematical skills and understanding of these concepts. Unfortunately, it seems that the specific calculations he used are not readily available.

In order to make a proper comparison between the different equations, it would be necessary to have a detailed understanding of the assumptions and approximations made in each case. This can be a complex and technical process, but it is an important step in understanding the underlying principles and limitations of each approach.

Overall, it is important to continue exploring and improving upon our understanding of energy levels in atoms and other systems. This requires careful analysis and consideration of all available data and theories. I hope this information helps in your search for the calculations you are seeking.
 

1. How do energy levels affect an atom’s behavior?

Energy levels play a crucial role in determining an atom’s behavior. The electrons in an atom occupy different energy levels and can jump between levels by either absorbing or emitting energy. This movement of electrons is what leads to the unique chemical and physical properties of different elements.

2. How can we measure the energy levels of an atom?

The energy levels of an atom can be measured using spectroscopy techniques. By analyzing the wavelengths of light absorbed or emitted by an atom, scientists can determine the energy levels of its electrons. This information is crucial in understanding the electronic structure of atoms and molecules.

3. What factors influence the energy levels of an atom?

The energy levels of an atom are influenced by several factors, including the atomic number, distance from the nucleus, and the presence of other nearby atoms. These factors can affect the amount of energy required for an electron to jump between levels and can also cause shifts in the energy levels themselves.

4. How does the arrangement of electrons in an atom’s energy levels affect its chemical properties?

The arrangement of electrons in an atom’s energy levels determines its chemical properties, such as reactivity and bonding behavior. The number of electrons in the outermost energy level, known as the valence electrons, is particularly important in determining an atom’s chemical behavior.

5. How can we use energy level diagrams to understand the behavior of atoms?

Energy level diagrams are graphical representations of an atom’s energy levels and the electrons within them. By studying these diagrams, we can understand how electrons are arranged and how they interact with each other and the nucleus. This helps us predict and explain the behavior of atoms in various chemical and physical processes.

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