(Specifically economic terms that may be unfamiliar to the reader are defined in the glossary, Sec. 13.10. These terms are identified by sans serif font in the text the first couple of times they are used.)

The overall aim of the discipline of econophysics is to apply the methods of mathematical physics to problems of economics. Probably the most basic phenomenon connecting economics and physics is Brownian motion, as analyzed by Louis Bachelier (1900) in his prescient Ph.D. thesis. Fast forwarding 100 years, a nice recent introduction to econophysics is the book by Mantegna and Stanley (2000). A classic book that brings together famous works by Bachelier, Mandelbrot, Osborne, and Cootner is one edited by Cootner (1964). Two recent books that (1) demonstrate how statistical physics techniques can be effectively applied to the economic problem and (2) extend notions that are developed in the Cootner book, are those of Bouchard and Potters (2000) and Voit (2001). Another physical effect used to advantage in economics is the heat equation. Using this in conjunction with the Ito calculus, Black and Scholes (1973) formed their famous valuation model. See also in this regard Merton (1974). Entropic uses in valuation have been advanced by Hawkins et al. (1996), and Hawkins (1997). A good example of the current state of econometrics, in general, in financial markets is Campbell et al. (1997). A wealth of further references on econophysics may be found in these books and on the World Wide Web.

This book has been concerned with generating wave equations, such as the SWE, that govern the fluctuations in physical data.