The magnetic moment of an electron

The magnetic moment of an electron is a fundamental property related to its spin and charge. It arises due to the electron’s intrinsic angular momentum, or spin.

In the absence of electromagnetic field is applied, the Hamiltonian of an electron is given by

When an electromagnetic field is applied, the Hamiltonian becomes

The magnetic field B in terms of vector potential A is defined as

Now we consider the second term of equation ii

represents magnetic moment due to orbital motion. Also

represents the intrinsic magnetic moment due to spin. The negative sign indicates that the direction of the magnetic moment is opposite to the direction of the angular momentum due to the negative charge of the electron. Now let us introduce gyromagnetic ratio = orbital magnetic moment/ angular momentum

where 𝜇_B = eℏ/2mc is known as Bohr's magneton

In general gyrometric ration is expressed as

𝛾 = ge/ 2mc where g is spectroscopic splitting factor called Lande's factor and it's value is

g= { 1 for 𝛾_L = g_L

= { 2 for 𝛾_S = g_S

This kind of notation is common in various fields such as physics, engineering, or mathematics, where the value of a parameter is defined based on certain conditions or inputs.

This note is a part of the Physics Repository