Spin-orbit interaction Definition and 17 Threads

Below is the derivation of E1so, the first-order correction to the Hamiltonian due to spin-orbit coupling of the election in hydrogen atom. My question is whether it's valid to use [6.64] (see below). ##<\frac{1}{r^3}>## I believe is ##<\psi_{nlm}|\frac{1}{r^3}|\psi_{nlm}>##, but ##\psi_{nlm}##...

I'm simulating on code the tight-binding sp3s* bandstructure of certain semiconductors, such as GaAs, AlP, InP, ZnSe, etc. with spin-orbit coupling at a temperature of T = 0 K but I'm having trouble at finding the corresponding spin-orbit splitting parameters. For example, I've found in this...

For an electron in the orbital characterized by ##l=0## we have ##j=0\pm1/2## and so ##J^2=j(j+1)## gives ##J^2=3/4## and ##-1/4## (normalized to ##\hbar^2##). Finally, ##L.S=1/2(J^2-L^2-S^2)## results in ##L.S=0## and ##-1##. However, according to ##L.S=l_xs_x+l_ys_y+l_zs_z## we find ##L.S=0##...

I was studying the spin-orbit interaction and the Zeeman effect, and came across the concept of optically active electrons. Initially I got the idea that an optically active electron is any unpaired electron. But then, while trying to understand the Zeeman effect in a Cadmium atom, for which...

Hello. I have studied about DWBA (distorted wave born approximation). But, I do not know the physical meaning of "DWBA without spin-orbit interaction". I think, I can not understand about meaning of spin-orbit. How can I understand "without spin-orbit intertaction". Thanks.

Hi, I have read that Hund's rules are valid for Atoms with low z. Because the third Hund's rule is build of Russell-Saunders coupling. Can I still use the first and second Hund's rule for heavy atoms and jj-coupling( for the third rule)? Or how can I know the groundstate for an atom with large...

Electric and magnetic parts of Maxwell's equations are kind of similar, so physical effects relating these properties have many 'dual' analogues - with exchanged places. For example in Aharonov-Bohm effect, the phase of charged particle depends on side of magnetic flux tube it comes through...

Homework Statement (a)Find splitting between F=0 and F=1 in hydrogen (b) Find the constant ##A## and nuclear magnetic moment Homework EquationsThe Attempt at a Solution Hyperfine splitting is given by: H_{hf} = \frac{A}{2} \left[ F(F+1) - I(I+1) - J(J+1) \right] The intervals are given by...

In all the places where Spin-Orbit interaction is discussed, the equations are derived by going to electron's rest frame and considering the interaction of nucleus' magnetic field with electrons spin magnetic moment. But from SR, we know that there as to be an explantion from the nucleus's rest...

Hello! This is my first time posting, so please correct me if I have done anything incorrectly. There's something that I don't understand about the spin-orbit interaction. First of all I know that [\hat{S} \cdot \hat{L}, \hat{L_z}] \ne 0 [\hat{S} \cdot \hat{L}, \hat{S_z}] \ne 0 so this means...

Hi, In many quantum physics books I see questions such as "what is the spin-orbit interaction in this case?" Sorry if this seems like a dumb question, but what do they mean by this? Do they mean the ENERGY of the spin-orbit interaction or something else? Also, could anyone give (or write a...

Fron wiki: spin–orbit interaction causes shifts in an electron's atomic energy levels due to electromagnetic interaction between the electron's spin and the magnetic field generated by the electron's orbit around the nucleus. This is detectable as a splitting of spectral lines. The...

Hi, It never occurred to me before, but when you derive the spin-orbit Hamiltonian as a perturbation to the hydrogen Hamiltonian, you imagine your electron orbiting around the nucleus, and of course that's not the correct picture because of the electromagnetic radiation that leaks out. So I...

Homework Statement The spin-orbit interaction splits the hydrogen 4f state into many (a) Identify these states and rank them in order of increasing energy. (b) If a weak external magnetic field were now introduced (weak enough that it does not disturb the spin-orbit coupling), into how many...

Homework Statement List all of the elements through calcium that you would expect not to have a spin-orbit interaction that splits the ground state energy. Explain. Homework Equations Not quite sure, but I'll list a few. If there are two electrons: L=|l1-l2| to |l1+l2| S=|s1-s2| to...

For a particular energy level in hydrogen, with quantum numbers n and l, one will find when considering the spin-orbit interaction, the level is split into two fine structure levels with energy separation: \Delta E_{s.o.}=\beta_{nl}(l+1/2) I was trying to prove this result. The spin of an...

Hi, I'm having a little problem understanding why splitting occurs in an atom. For example when you look at the line spectra for Sodium-D, then two lines appear very close together. I understand that there is a magnetic interaction where the magnetic field has been generated by the orbital...