Weak field zeeman effect, why don't we still use degenerate perturbation theory?

In summary, the spin orbit coupling partially removes the degeneracy of the spin orbit Hamiltonian, but not completely. It is still possible to use degenerate perturbation theory, but only up to first order. Higher order or exact energy eigenvalues will result in a non-degenerate spectrum. However, this approach may not be accurate if the magnetic field energy splitting is larger than the second order splitting caused by the spin orbit Hamiltonian.
  • #1
alemsalem
175
5
the spin orbit coupling removes the degeneracy but not completely, should we still use the degenerate perturbation theory. is it because of relativistic corrections?

Thanks!
 
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  • #2
Since nobody is answering I will say what I think the answer is although I'm not very sure, please correct me if I'm wrong.
the spin orbit Hamiltonian is only degenerate up to first order in perturbation theory, higher order ( or exact) energy eigenvalues will not give a non-degenerate spectrum.

I'm not sure about this answer because then the magnetic field energy splitting has to be smaller than the SECOND order splitting due to Spin orbit hamiltonian.

I hope I'm making sense.
 

FAQ: Weak field zeeman effect, why don't we still use degenerate perturbation theory?

1. What is the Weak Field Zeeman Effect?

The Weak Field Zeeman Effect is a phenomenon in quantum mechanics where the spectral lines of an atom or molecule are split into multiple components when exposed to a weak magnetic field. This effect is caused by the interaction between the magnetic moment of the electron and the magnetic field.

2. How does degenerate perturbation theory relate to the Weak Field Zeeman Effect?

Degenerate perturbation theory is a mathematical method used to calculate the energy levels of an atom or molecule in the presence of a weak magnetic field. It takes into account the effects of the magnetic field on the degenerate energy levels of the system, resulting in the splitting of spectral lines observed in the Weak Field Zeeman Effect.

3. Why is degenerate perturbation theory no longer used to explain the Weak Field Zeeman Effect?

While degenerate perturbation theory is a useful tool in understanding the Weak Field Zeeman Effect, it has limitations. It only works for weak magnetic fields, and it does not take into account more complex interactions between the electron and the magnetic field. As a result, more advanced theories and techniques have been developed to better explain this phenomenon.

4. What are some alternative theories used to explain the Weak Field Zeeman Effect?

Some alternative theories used to explain the Weak Field Zeeman Effect include the Paschen-Back effect and the Breit-Rabi formula. These theories take into account more complex interactions and are better suited for strong magnetic fields.

5. Is the Weak Field Zeeman Effect still relevant in modern science?

Yes, the Weak Field Zeeman Effect is still relevant in modern science. It is used in various fields such as spectroscopy, astrophysics, and quantum computing. It allows scientists to study the properties of atoms and molecules and make precise measurements of magnetic fields.

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