What is the speed of light doing in the spin half hamiltonian?

  • #1

Main Question or Discussion Point

I'm currently reading Sakurai's 'Modern Quantum Mechanics' (Revised Edition) and at page 76 he introduces a spin half hamiltonian

[tex] H = - (\frac{e}{mc}) \vec S \cdot \vec B.[/tex]

But what is c doing in this hamiltonian? Clasically the energy of a magnetic moment in a magnetic field is

[tex] E = - \vec \mu \cdot \vec B = - \frac{e}{2m} \vec S \cdot \vec B[/tex]

and as far as i know what one does to go to QM is to introduce the g-factor. What am I missing here?
 

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
12,986
541
Standard question, standard answer: the spin-orbit coupling is a specially relativistic effect, even though the spin notion itself can be derived without special relativity. The <c> comes from the Dirac equation.
 
  • #3
Bill_K
Science Advisor
Insights Author
4,155
195
Say what? If this term is spin-orbit coupling, where is L??

The c comes about because according to Dirac the magnetic moment μ of the electron is -eħ/2mc, or -e/mc times the spin ħ/2.
 
  • #4
ah, thanks. I guess I have to be reading up on that then.
 
  • #5
dextercioby
Science Advisor
Homework Helper
Insights Author
12,986
541
Sorry, not paying attention. Disregard my post above.

If the <c> is there or not must be in the end a matter of convention, just like the as the case of CGS vs MKS in electromagnetism.
 
Last edited:

Related Threads on What is the speed of light doing in the spin half hamiltonian?

Replies
7
Views
1K
Replies
6
Views
2K
  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
7
Views
2K
Replies
5
Views
9K
  • Last Post
Replies
2
Views
2K
Replies
18
Views
3K
Replies
5
Views
728
  • Last Post
Replies
1
Views
417
Top