QM: Spin-orbit and wavefunctions for H

In summary, the speaker is asking for help with evaluating the dipole moment for the hydrogen atom with spin-orbit coupling. They are unsure if they can use the regular wavefunctions or if they need to calculate perturbed wavefunctions due to the change in eigenstates caused by spin-orbit coupling. They express concern about the length of this task.
  • #1
Niles
1,866
0

Homework Statement


Hi all.

I wish to evaluate the following dipole moment

[tex]
<1| x |2>,
[/tex]

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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  • #2
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.
 
  • #3
This is what I feared.. it seems like a pretty long task.
 

1. What is spin-orbit coupling in quantum mechanics?

Spin-orbit coupling is a phenomenon in quantum mechanics where the spin of an electron is affected by its orbital motion around the nucleus. This interaction between the electron's spin and its motion results in a splitting of energy levels, which can be observed in atomic spectra.

2. How does spin-orbit coupling affect electron behavior?

Spin-orbit coupling affects electron behavior by causing the electron's spin to align with its orbital motion, resulting in a net spin and orbital angular momentum. This can lead to changes in energy levels and can also affect the direction of electron spin in certain experiments.

3. What are wavefunctions in quantum mechanics?

Wavefunctions are mathematical functions that describe the probability amplitude of finding a particle in a particular state or location. In quantum mechanics, the square of the wavefunction gives the probability of finding the particle in a specific location or state.

4. How do wavefunctions relate to spin-orbit coupling in the context of "H"?

In the context of "H," wavefunctions are used to describe the energy states of the hydrogen atom. Spin-orbit coupling is a term that describes the interaction between the spin and orbital motion of the electron in the hydrogen atom, which can affect the overall wavefunction of the atom.

5. Can spin-orbit coupling be observed in other particles besides electrons?

Yes, spin-orbit coupling can be observed in other particles besides electrons, such as protons and neutrons. It is a fundamental phenomenon in quantum mechanics that occurs whenever a particle has both spin and orbital motion, and can affect the behavior of many different types of particles.

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