QM: Spin-orbit and wavefunctions for H

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SUMMARY

The discussion focuses on evaluating the dipole moment <1| x |2> for stationary states of the hydrogen atom while considering spin-orbit coupling. Participants agree that the unperturbed wavefunctions for hydrogen cannot be used directly, as spin-orbit coupling alters the eigenstates and shifts energy levels. Consequently, it is necessary to calculate the perturbed wavefunctions to accurately determine the dipole moment, indicating a more complex and time-consuming task ahead.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of hydrogen atom wavefunctions
  • Knowledge of spin-orbit coupling effects
  • Familiarity with dipole moment calculations
NEXT STEPS
  • Calculate perturbed wavefunctions for hydrogen under spin-orbit coupling
  • Explore the implications of spin-orbit coupling on energy levels
  • Review dipole moment evaluation techniques in quantum mechanics
  • Study the mathematical framework of perturbation theory
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying atomic physics and the effects of spin-orbit coupling on hydrogen atom properties.

Niles
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Homework Statement


Hi all.

I wish to evaluate the following dipole moment

<br /> &lt;1| x |2&gt;,<br />

where |1> and |2> are stationary states of the hydrogen atom when one accounts for spin-orbit coupling. I am a little unsure of if I am allowed to use the "normal" unperturbed wavefunctions for hydrogen in this case, or if the wavefunctions change because of spin-orbit?
 
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I don't think so, the spin-orbit coupling will shift your energies, which means that the eigenstates have changed.

So |1> and |2> are not the same as the regular ones...I think you're going to have to calculate the perturbed wave functions.
 
This is what I feared.. it seems like a pretty long task.
 

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