Nuclear magnetic resonance (NMR) is an important example in the dynamics of two-state systems because it is involves the exact solution to a time dependent Hamiltonian. The NMR phenomenon is achieved by placing a nucleus in a strong, static field B0 (the "holding field") and then applying a weak, transverse field B1 that oscillates at some radiofrequency ωr.[3] Explicitly, consider a spin-1/2 particle in a holding field B 0 z ^ {\displaystyle B_{0}\mathbf {\hat {z}} } and a transverse rf field B1 rotating in the xy-plane in a right-handed fashion around B0: