Spin States

Open Source Physics spin state program models a particle with spin 1/2 in a magnetic field.

Hamiltonian

The Hamiltonian for a system with spin in a magnetic field depends on the interaction between the magnetic dipole moment u and the magnetic field B.

H = - u . B

If B is in the z-direction and has magnitude B0 and if the particle has spin 1/2 (that is, an electron in a uniform magnetic field B0) then the Hamiltonian can be written

 

H = - e  B0 Sz/( m c)

where  the spin operator Sz is h_bar/2 times the following matrix:

 1   0
 0  -1

 

It is easy to write down the Hamiltonian eigenvalues and the eigenfunctions.  Why?  What are the eigenvalues?