NMR is inherently a quantum phenomenon since it involves nuclear spin. However, on the other hand, it is difficult know how to describe spin as a wave function. In practice, this detail is bypassed and the wave function is based on whether the spin is up or down. Thus, we can write the spin wave function as a vector. Starting with this description we can use the Pauli spin matrices to describe the various directional spin states. This is important since the NMR experimental configuration involves a rotation from an initial z-axis conformation to the x,y plane where a rotation occurs under control of the external magnetic field, B0.
The operations in NMR are all rotations. Thus, the form of the operators is quite simple compared to the quantum mechanical description of vibrations. By studying NMR time-dependent operators one can come to a good understanding of how time-dependent operators function.
The relaxation time can be decomposed into two contributions, known as longitudinal and transverse relaxation. Longitudinal relaxation refers to the process by which the spins return to the z-axis orientation after they have been rotated into the x,y plane. One can picture the spins spiraling upwards towards their original vector orientation. The time required for this relaxation is known as the T1 time or population relaxation time. Transverse relaxation refers to the time required for the spins to fan out or spread out in the x,y plane following rotation. The spins all have slightly different magnetic environments and therefore they tend to rotate at different rates. Because of this tendency the spins lose coherence. The NMR signal arises because of the collective motion of the spins rotating as a vector in the x,y plane. This motion is detected by the induction coils of the receiver. After a period of time known as the T2 time the spins lose coherence. They are no longer pointing in one direction and all signal decreases until eventually it is lost.
The T1 and T2 relaxation times in NMR can be determined by two experiments known as inversion recovery and spin echo, respectively. Inversion recovery was discussed briefly in the previous video on relaxation. Here we focus in a bit more detail on the spin echo experiment. This experiment and the technique of refocusing spins is extremely important for more advanced NMR pulse sequences.
We can summarize the important terms used in the calculation of the effects of the NMR pulse sequences. The quantum mechanical approach based on rotation using matrix mechanics. This includes the basic 90o pulse using a radiofrequency field, B1. The rotations in the magnetic field, B0 and the conventions for rotation used in both the matrix (operator) and vector methods for predicting the effect of pulse sequences.
The direct product is the matrix method used to calculate the effects of pulse sequences on two spins simultaneously. This is essential in order to understand coherences, J-coupling and transfer of magnetization through space (dipolar coupling). All of these terms as important in multi-dimensional NMR used for determination of protein and nucleic acid structure./h2>
