# Why electron spin being anti-parallel to the orbital angular momentum gives lower energy than the electron spin being parallel to the angular

Take hydrogen atom as example. The 2P orbital will split due to spin-orbit coupling to the $^{2}P_{3/2}$ and $^{2}P_{1/2}$ terms. The term $^{2}P_{1/2}$ has anti-parallel orientation of electron spin and orbital angular moment and is lower in energy than the $^{2}P_{3/2}$ which has parallel spin and orbital angular moment.

Why is that and not the other way around? From electrodynamics we know that magnetic potential energy is minimal when two magnetic dipoles are parallel which confuses me here.

• Are you sure on the statement about aligning dipoles? Dipoles align with magnetic fields, and the field of a dipole is such that a neighbouring dipole will anti-align. – diracula Mar 6 '17 at 21:46
• Hm... no I am not sure about that. Looks like I assumed that since magnetic dipole in external homogeneous magnetic field will align to be parallel then that also must be true for the external field created by another magnetic dipole. I tried to find some article about magnetic dipole-dipole energy and when it is minimum but I couldn't... all I find is magnetic dipole energy in external field. If you have some helpful link please let me know or maybe you could write answer below with basic formulas that proves this. Thanks for your comment. – matori82 Mar 7 '17 at 1:08