- 160

- 0

The g-factor has an appearance of [tex]\frac{e}{2M}[/tex]. It differs only very small to what we expect from the notation of the Bohr Magneton. So the question arises whether the g-factor is intrinsically related to energy.

It is possible to satisfy for instance that:

[tex]\sum^{N}_{i=1} \vec{\mu}_i \propto \frac{eh}{2Mc}[/tex] 1.

Where [tex]\mu_B= \frac{eh}{2M}[/tex] is the Bohr magneton. Equation 1. is simply the sum of magnetic moments where it measures the gyromagnetic ratio of a particle induced in a magnetic field.

The energy is given by the Lande' g-factor as a magnetic interaction on the system. This can be given as

[tex]\Delta E = \frac{eh}{2Mc}(L+2S) \cdot B[/tex]

Since

[tex]\sum^{N}_{i=1} \vec{\mu}_i \propto \frac{eh}{2Mc}[/tex]

Then

[tex]\sum_{i=1}^{N} E_i = \sum_{i=1}^{N} (\frac{eh}{2Mc})_i (L+2S) \cdot B \propto \sum_{i=1}^{N} \mu_i (L+2S) \cdot B[/tex]

If the calculation is right, then one can easily assume that energy is related to the sum (of) some periodic functions of the appearence of a magnetic moment and the g-factor is proprtional the magnetic moment.