Spin-Orbit Coupling, PHYS 372

This video describes the spin-orbit perturbation Hamiltonian and its effect on the fine structure of hydrogen. It is meant as a companion for Griffiths & Schroeter, Introduction to Quantum Mechanics, Section 7.3.2. Any textbook references are to that book.
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Here are several more videos from my course PHYS 372, Quantum Theory at Hope College: • Lectures on Quantum Me...
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[@steveagnew3385]

Thanks so much for this. Your derivation shows so nicely that E_fs =n(j) { E_n/(2m_e c) } E_n , that the spin-orbit splitting is proportional to energy level by the ratio of the energy level to the relativistic energy of the electron.
You avoided incorporating the fine-structure constant, which most other derivation include. Including the fine-structure constant obscures this simple relationship. This relation shows how the fine-structure constant can vary over cosmic time and yet the spin-orbit splitting will remain proportional to the energy level to first order. For the collapsing universe, E_n/(m_e c) is constant to first order even though both c and alpha vary slowly over cosmic time...

[@user-ml9ib1lm3r]

very helpful , thank you very much !

[@RogerTerrill]

Love it!!! Thanks so much!!!

[@ashwanthk4550]

one doubt as, why there is no splitting of s orbital in the spin-orbit coupling, can you explain conceptually related to the shape of s orbital or such.

[@lallawmsangkhawzawl999]

What happens when a magnetic field is applied to the spin - orbit coupling ?

[@indrashispowali]

mindblown

[@josephcoon5809]

Darn it...RUclips deleted my question...
Is r affected by the relativistic velocities of the electrons or the curvature of space created by the mass of the proton? I imagine what we observe as the radius of the shell would actually be smaller than reality.

[@stephenremillard1]

Thank you for this question. The relativistic speed of electrons leads to energy splitting between s,p,d... levels of the same principal quantum number. The relativistic orbital velocity also means that the electron mass should include the usual relativistic gamma factor, which is then incorporated into the Bohr radius, resulting as you suggest, in a smaller relativistic Bohr radius. I believe this effect is more pronounced with heavier elements. Details about it would be covered in a text on relativistic quantum chemistry or atomic physics. Intriguing question about the space-time curvature from the proton mass. Because of the mass scale (and more so my admitted lack of familiarity) that's something I don't know about.

[@josephcoon5809]

@@stephenremillard1 I appreciate your response. I found a renewed interest in physics and math, and my head is churning with many new ideas that constantly bump into each other.
Lately, I’ve been trying to find anything about photon polarity mode and how it is affected by traveling near electron fields. I can’t find anything that sufficiently explains why reflected light is polarized parallel to the surface and refracted light is polarized perpendicular to that surface.
It seems as if it may be due to precessional forces if considering classical physical mechanics, or a disparity in the manner in which the field destructively interferes with itself depending on how the light wave interacts with the surface of an electron field verses traveling through the field.
I don’t know if any of that made sense. Like I said, I have all kinds of ideas clashing in my head.
Thanks again for the video.

[@josephcoon5809]

Also, I apologize if my question is academic. I haven’t taken a physics course in over two decades.