The optical Bloch equations for a collection of spin-1/2 particles can be derived from the time dependent Schrödinger equation for a two level system. Starting with the previously stated Hamiltonian i ℏ ∂ t ψ = − μ σ → ⋅ B → ψ {\displaystyle i\hbar \partial _{t}\psi =-\mu {\vec {\sigma }}\cdot {\vec {B}}\psi } , it can be written in summation notation after some rearrangement as