## The non interacting magnetic system

$$\mathcal{H}=-g\mu_B\sum^N_{i=1}\textbf{S}_i\cdot\textbf{H}$$
- 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

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