Wednesday, May 15, 2019

electromagnetism - Real QM cause of magnetic dipole moment


I have read these questions:


Relation between magnetic moment and angular momentum -- classic theory


Why is the electron magnetic moment always parallel to the spin for an electron?



Does a magnetic field do work on an intrinsic magnetic dipole?


Isn't the spin only a synonym for the existence of a magnetic dipole moment and its direction?


Does a magnetic field arise from a moving charge or from its spin, or both?


Relationship Between Magnetic Dipole Moment and Spin Angular Momentum


where it says:



A spinning charged particle constitutes a magnetic dipole. Its magnetic dipole moment μ is proportional to its spin angular momentum S: μ=γS the proportionality constant γ is called the gyromagnetic ratio.



Is the magnetic field/force just a relativistic electric field/force or is there a fundamental difference?


where the comments say:




Because in a magnet, the atomic electrons are moving around their respective nuclei constituting a dipole and the dipoles are aligned in same direction to give net magnetic dipole moment.



So one is saying that magnetic dipole moment is caused by spin angular momentum, which is the intrinsic spin of an electron, the other one says that magnetic dipole is cause by electrons orbiting (orbital angular momentum) the nuclei (of course as per QM they are not classically orbiting).


So which one is right?


None of these questions says whether the magnetic dipole moment at QM level is caused by the intrinsic spin of electrons or the bound electrons' (OAM) orbiting (as per QM existing at a certain energy level) around the nuclei.


Question:



  1. Which one is right, is the magnetic dipole moment as per QM caused by the intrinsic spin of electrons or by electrons orbiting (OAM) the nuclei existing around the nuclei at a certain energy level?




Answer



Spin and orbital angular momentum are two independent contributions to the total angular momentum. The ratio between angular moment and magnetic moment is called the g-factor. For the magnetic moment operator one has $\vec M /\mu_B = g_L \vec L + g_S \vec S$. The electron spin contributes with g=2 and orbital moment with g=1. The expectation value of this operator gives the magnetic moment. $\mu_B$ is the Bohr magneton.


No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...