Quantum Mechanical Basics of NMR-Spectroscopy

In this lecture, fundamental quantum-mechanical concepts are introduced that form the basis for the understanding and the design of advanced nuclear magnetic resonance experiments. A number of different approaches are discussed how to describe spin systems, how to initialize them, how to calculate their time evolution and how to obtain expectation values of experimentally interesting observables: (a) state functions and Schrödinger equation, (b) magnetization vectors and the Bloch equations, (c) density operator and Liouville-von Neumann equation and (d) Cartesian product operator formalism. An important goal of the lecture is to establish the links between these different formalisms, to clarify the situations in which they are applicable and also the limits where they cannot be applied. Important terms of the rotating frame Hamiltonian are introduced such as frequency offsets, radiofrequency pulses and J couplings. In addition, the concepts of Average Hamiltonian Theory are discussed (effective propagator, effective Hamiltonian, average Hamiltonian, toggling frame), which provide powerful tools for the analysis and the design of modern multiple-pulse sequences. Concrete examples that are analyzed using these approaches include the Stern-Gerlach experiment, the precession of a spin ½ particle in an external magnetic field, the effects of chemical shift, pulses and couplings and coherence transfer in TOCSY and INEPT-type experiments.

Upon successful completion of this module, students are able to apply the basic concepts and mathematical descriptions of quantum mechanics to NMR spectroscopy. They are able to analyze known NMR experiments. Furthermore they are able to evaluate different ways and concepts of mathematically describing these NMR experiments. Finally they are also able to create new NMR experiments.

Lectures in quantum mechanics; theoretical knowledge (and practical experience) in NMR spectroscopy.

The application of basic concepts and mathematical descriptions of quantum mechanics to NMR spectroscopy are presented during the lecture. The blackboard as well as presentations using a beamer are used during this lecture. It is important, that students practise in particular the mathematical calculations of quantum mechanical descriptions themselves. Therefore additional calculations are provided on the corresponding moodle site; as well as further information for self-study.

Powerpoint, black board,

1) Maurice Goldman: "Quantum Description of High-Resolution NMR in Liquids"
2) Richard R. Ernst: "Principles of Nuclear Magnetic Resonance in One and Two Dimensions"
3) James Keeler: "Understanding NMR Spectroscopy"

In the written examination (90 minutes) students demonstrate by answering questions and calculating quantum mechanical descriptions under time pressure and by only using the helping material attached to the exam, that they are able to analyze spin systems, their evolution, and the corresponding observables in given NMR experiments.