I Lower energy levels with Dirac/Pauli theory than Schroedinger theory?

  • I
  • Thread starter Thread starter Juli
  • Start date Start date
  • Tags Tags
    Dirac Pauli
Juli
Messages
24
Reaction score
6
TL;DR Summary
Lower energy levels with dirac/pauli theory than Schroedinger theory
Why do the enery levels calculated with the Dirac/Pauli euqations always lie lower than the results calculated with the Schrödinger equation?
I assume it has to do something with relativistic effects and the changing masses because of this.
 
Physics news on Phys.org
Please provide a specific example (or a reference to such an example)
 
hutchphd said:
Please provide a specific example (or a reference to such an example)
A specific example would be the hydrogen atom. I have linked a photo of what I mean.
Why are the corrected energys always lower? The relativistic parts are obviously taking up some energy and my question is where it goes. I don't think it's spin-orbin couling, since it just splits the levels up, some go higher, some lower. I think it's the kinetic and potential energy-terms. But why exactly? It probably has to do something with the relativistic mass, but aren't we using the rest mass in the Pauli-equation?

Screenshot 2025-01-17 160501.png
 
Juli said:
It probably has to do something with the relativistic mass, but aren't we using the rest mass

This effect should not be related to the relativistic mass. Relativistic mass is a deprecated concept that is no longer used to interpret special relativity, it is just a Lorentz factor in front of the mass.

Juli said:
A specific example would be the hydrogen atom. I have linked a photo of what I mean.
Why are the corrected energys always lower? The relativistic parts are obviously taking up some energy and my question is where it goes. I don't think it's spin-orbin couling, since it just splits the levels up, some go higher, some lower. I think it's the kinetic and potential energy-terms. But why exactly?

It is probably not true (as far as I know) that relativistic systems have lower energies than the non-relativistic ones. It is probably not even true for the hydrogen atom. As far as you have shown it is true for the first two levels of the hydrogen atom. In that case, yes it is due to the relativistic corrections to the kinetic energy as shown by the weakly relativistic calculation (at first order it's negative and larger than the other fine structure factors for the ground state and some of the first excited states).

Edit:

Juli said:
but aren't we using the rest mass in the Pauli-equation?

Also no idea what you mean by Pauli equation here, that's just Schrödinger's equation but with spin.
 
Last edited:
Juli said:
A specific example would be the hydrogen atom. I have linked a photo of what I mean.
Where does this photo come from? We need a reference.
 
  • Like
Likes Lord Jestocost
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
Back
Top