It is inconvenient to deal with a time-dependent hamiltonian. To make H ^ ^ time-independent requires a new reference frame rotating with B 1 , i.e. rotation operator R ^ ^ ( t ) on | Ψ Ψ ( t ) ⟩ ⟩ , which amounts to basis change in Hilbert space. Using this on Schrödinger's equation, the Hamiltonian becomes: