Open Source Physics spin state program models a particle with spin 1/2 in a magnetic field.
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:
It is easy to write down the Hamiltonian eigenvalues and the eigenfunctions. Why? What are the eigenvalues?