can someone please explain me in simple physics that why spin-orbit coupling is relativistic?
A short summary: there is no derivation of spin-orbit coupling (or even the spin) in "classical" quantum mechanics by the principle of correspondence. You can of course conclude the phenomenon from experiments.
However, an "ab initio" derivation of the phenomenon is possible if you reduce the relativistic Dirac equation to the matter terms (neglecting anti-matter components). The resulting equation is often referred to as the "Pauli equation" (https://en.wikipedia.org/wiki/Pauli_equation#Relationship_with_the_Schr%C3%B6dinger_equation_and_the_Dirac_equation)and contains spin-orbit coupling (and other corrections like the "Darwin term").
So, since the origin of that term is the relativistic equation, it's called a rekativistic term.
Maybe This can help you:
https://www.quora.com/Why-is-electronic-spin-orbit-coupling-a-relativistic-effect-if-the-electronic-spin-and-orbit-are-non-relativistic-properties
A short summary: there is no derivation of spin-orbit coupling (or even the spin) in "classical" quantum mechanics by the principle of correspondence. You can of course conclude the phenomenon from experiments.
However, an "ab initio" derivation of the phenomenon is possible if you reduce the relativistic Dirac equation to the matter terms (neglecting anti-matter components). The resulting equation is often referred to as the "Pauli equation" (https://en.wikipedia.org/wiki/Pauli_equation#Relationship_with_the_Schr%C3%B6dinger_equation_and_the_Dirac_equation)and contains spin-orbit coupling (and other corrections like the "Darwin term").
So, since the origin of that term is the relativistic equation, it's called a rekativistic term.
The spin-orbit coupling is called relativistic because the magnetic field B coupled to the spin S of the electrons in the with orbital angular momentum is due to the electric field of the nucleus,i.e. it is not due to an hyperfine magnetic field of the nucleus. The form to understand the transformation of the electric field E in a magnetic field B is using the Lorentz relativistic transformations.
The shift of energy is proportional to S.L and also to atomic number Z4 to fourth power. This result can be obtained also applying the relativistic formulation of Quantum Mechanics, i.e. the Dirac equation and it coincides very well.
Thus the relativistic origin of the LS spin-orbit is very clear.
Experimentally spin was discovered in Stern-Gerlach experiment in 1922 and George Uhlenbeck and Samuel Goudsmit proposed the idea of "spin" to explain certain spectroscopic features.
In non-relativistic quantum mechanics one has to introduce spin by hand. In relativistic quantum mechanics, electron spin is predicted by the Dirac equation. So the concept of "intrinsic spin" is a relativistic concept. It originates in the relativistic Dirac equation in a natural way. Therefore spin-orbit interaction is also fundamentally relativistic.
- Badges
- Science topic
- Similar topics
- Physics
- Condensed Matter Physics