Bloch equations

The Bloch equations are a system of equations of motion of two-level systems. They allow a physical interpretation of the paramagnetic resonance effect in nuclear magnetic resonance and electron paramagnetic resonance. The Bloch equations were first published in 1946 by Felix Bloch.

The Bloch equations are valid for liquids, but only limited for solids. Make the equations of motion is for the entire nuclear and electron magnetization of the sample under the influence of external magnetic fields and are denominated in vector notation:

Of the first term of the right-hand side describes the motion of the magnetization in the magnetic field H is the gyromagnetic ratio of the nuclei and the electrons. The last three terms on the right side of the equation describing the paramagnetic relaxation, which tends to a steady state value by the interaction of the particles with one another and with its molecular environment. The vectors are the unit vectors in x-, y- and z-direction. is the spin-lattice relaxation time and the transverse relaxation time ( spin-spin relaxation). The external magnetic field is composed of two components, a strong constant magnetic field in the z direction and a perpendicular to the applied high-frequency magnetic field in the x direction.

It was later shown that these originally designed for Spin-1/2-Systeme equations of motion describe any other two-level system. Parts of the general " Pseudo-Spin-1/2-Systems " associated with spin components and discusses the interaction with external fields such as magnetic interactions. In the semi-classical radiation theory, the spin components correspond to the ground or excited state of a two- level atom, and the axes of the Bloch sphere provide information about the quantum mechanical coherence (x -, y - axis) and the population difference (z- axis ) of the system. The purpose adapted equations are called the optical Bloch equations.