# The non interacting magnetic system

by LagrangeEuler
Tags: interacting, magnetic
 P: 310 $$\mathcal{H}=-g\mu_B\sum^N_{i=1}\textbf{S}_i\cdot\textbf{H}$$ - The hamiltonian for a system of $$N$$ non-interacting magnetic moments in a an external magnetic field $$\textbf{H}$$. Why product $$\textbf{S}_i\cdot\textbf{H}$$ may only assume the values $$m_iH$$ where $$m_i=-S,-S+1,...,0,...,S-1,S$$? $$g$$ - Lande factor $$\mu_B=\frac{e\hbar}{2mc}$$ - Bohr magneton