\( \newcommand{\ket}[1]{\mbox{$|#1\rangle$}} \newcommand{\bra}[1]{\mbox{$\langle #1|$}} \newcommand{\cn}{\mbox{$\mathbb{C}$}} \newcommand{\rn}{\mbox{$\mathbb{R}$}} \newcommand{\knull}{\mbox{$|{\mathbf 0}\rangle $}} \newcommand{\bnull}{\mbox{$\langle {\mathbf 0}|$}} \newcommand{\sprod}[2]{\mbox{$\langle #1 | #2 \rangle $}} \newcommand{\ev}[3]{\mbox{$\langle #1 | #2 | #3 \rangle $}} \newcommand{\av}[1]{\langle #1 \rangle} \newcommand{\norm}[1]{\mbox{$\Vert #1 \Vert $}} \newcommand{\diad}[2]{\mbox{$|#1\rangle \langle #2 | $}} \newcommand{\tr}[1]{\mbox{$Tr\{#1\}$}} \newcommand{\sx}{\mbox{$\hat{\sigma}_x$}} \newcommand{\sy}{\mbox{$\hat{\sigma}_y$}} \newcommand{\sz}{\mbox{$\hat{\sigma}_z$}} \newcommand{\smx}{\mbox{$\left( \begin{array}{cc} 0 & 1 \\ 1 & 0\end{array} \right)$}} \newcommand{\smy}{\mbox{$\left( \begin{array}{cc} 0 & -i \\ i & 0\end{array} \right)$}} \newcommand{\smz}{\mbox{$\left( \begin{array}{cc} 1 & 0 \\ 0 & -1\end{array} \right)$}} \newcommand{\mat}[4]{\mbox{$\left( \begin{array}{cc} #1 & #2 \\ #3 & #4 \end{array} \right)$}} \newcommand{\col}[2]{\mbox{$\left( \begin{array}{c} #1 \\ #2 \end{array} \right)$}} \)

I wrote these notes as a postdoc at Penn, working on MRI. They were intended to provide a condensed but detailed overview of quantum mechanics necessary to understand some NMR phenomena that were of current research interest (so called multiple quantum coherence effects).

The notes cover a lot of relevant math and could probably be of interest to anyone learning about quantum mechanics so I've converted the LaTex source into a series of web pages and slightly adapted the formatting. I hope you find them useful.

This short lecture series has two main goals: 1. To introduce you to quantum mechanics at a level necessary for a good understanding of the fundamentals of nuclear magnetic resonance (NMR) and 2. To present the quantum mechanical description of NMR in sufficient detail so that you can understand multiple quantum coherence effects. The lectures will be split into two logical parts, first one dealing with the formalism of quantum mechanics and the second in which we will apply that formalism to NMR.

Firstly, the necessary mathematics will be presented in a precise although not mathematically strict way. Some familiarty with certain mathematical concepts is expected from the reader. While quantum mechanics is often considered hard to grasp, the mathematics that it is based on is often as simple as the mathematics of classical mechanics. Understanding of the mathematical concepts behind quantum mechanics helps build a physical intuition and enables easier understanding of the calculations. After the mathematics is out of the way quantum mechanics will be introduced in an axiomatic way. Examples will be given that relate to spin 1/2, i.e. NMR. Secondly, the concepts introduced in the first part of the series will be applied to a spin 1/2 system. This is the simplest possible case of a system described by quantum mechanics, yet it provides for most of the rich experimental features of NMR experiments.