ABSTRACT
In order to establish a foundation for relaxation theory, this chapter provides a background by introducing the concepts of spin-lattice and spin-spin relaxation. It looks at a simple example, which captures the basic principles of the nuclear spin relaxation without being directly applicable to any real physical situation. In nuclear magnetic resonance relaxation theory, stochastic processes (stochastic functions of time) are important. The relaxation rate is proportional to a transition probability. The weakness of the relevant interactions for spin 1/2 nuclei results in small transition probabilities and the spin-lattice relaxation processes being slow, typically on the millisecond to second time scale. The combination of the random walk and the anisotropic interactions gives rise to Hamiltonians for nuclear spins varying randomly with time. The effect of these random – or stochastic – interactions is to cause transitions, which are intimately connected with the nuclear spin-relaxation processes.
