Two-Dimensional (2D) NMR Methods

3 Product Operator Formalism

Rolf Boelens^* and Robert Kaptein

Department of Chemistry, Utrecht University, Padualaan 8, 3584 CH, Utrecht, The Netherlands^* Corresponding Author

3.1 Introduction

In quantum mechanics, measurable quantities are described by operators (see Appendix 3.A for an introduction to quantum mechanics and operators). A well-known example of an operator is the Hamiltonian operator (), which, when applied to a wave function describing a stationary state (an eigenfunction of ), yields the energy of that state:

(3.1)

When states are not stationary, for example in NMR due to irradiation with a radio-frequency (RF) source, a system can be described by the time-dependent Schrödinger equation:

(3.2)

The equation describes how evolves in time. Assume we have two stationary states and with energies and , then a solution for the wave function describing the system under ...