Linear Superposition of Hamiltonians

[wofsy]

The Hamiltonian for a spin 1/2 particle in 2 or more magnetic fields is the sum of its Hamiltonians for each field separately. For instance if I break a magnetic field into components in some coordinate system then the full Hamiltonian is the sum of the separate Hamiltonians for each co-ordinate magnetic field.

Can someone explain the Physics of why the Hamiltonians can be linearly superposed in this case?

 

[Ben Niehoff]

Because

$$H = -\vec \mu \cdot \vec B$$

and B obeys linear superposition.