On the analysis of high-resolution nuclear magnetic resonance spectra

Some new methods for analysing high-resolution nuclear magnetic resonance spectra are discussed and exemplified by the two-particle AB system. A brief summary is first given of the traditional (‘indirect’) method which evaluates the resonance frequencies as differences between the Hamiltonian eigenvalues, and the intensities as squares of the matrix elements of the dipole operator. The so-called ‘direct’ method is then discussed, which gives the resonance frequencies and intensities directly as solutions of a new eigenvalue problem, involving the derivation superoperator of the Hamiltonian. From the direct method the more elegant and compact correlation function method is developed, yielding the complete spectrum as a single entity. In all the methods the so-called level shift representation is also discussed, which may be advantageous for qualitative considerations of the spectrum and which is a convenient starting point for approximation methods. Mathematical concepts which may be new to the reader are explained in detail and exemplified.