As in the free precession case, the Hamiltonian is H = − μ σ ⋅ B {\displaystyle H=-\mu {\boldsymbol {\sigma }}\cdot \mathbf {B} } , and the evolution of a state vector ψ ( t ) {\displaystyle \psi (t)} is found by solving the time-dependent Schrödinger equation H ψ = i ℏ ∂ ψ / ∂ t {\displaystyle H\psi =i\hbar \,\partial \psi /\partial t} . After some manipulation (given in the collapsed section below), it can be shown that the Schrödinger equation becomes