Quantum Derivation of the Bloch Equations Excluding Relaxation

Abstract

The equation of motion of the density matrix of an ensemble of identical spin-1/2 nuclei subject to a rotating-frame radiofrequency field and Zeeman frequency offset is derived from the Schrodinger equation and shown to be equivalent to the magnetization differential equations originally proposed by Bloch (excluding relaxation). The quantum and classical differential equations are then integrated.