ABSTRACT
This chapter provides a comprehensive overview of the Bohmian
formulation of quantummechanics. It starts with a historical review
of the difficulties found by Louis de Broglie, David Bohm, and
John S. Bell to convince the scientific community about the validity
and utility of Bohmian mechanics. Then, a formal explanation
of Bohmian mechanics for nonrelativistic, single-particle quantum
systems is presented. The generalization to many-particle systems,
where the exchange interaction and the spin play an important role,
is also presented. After that, the measurement process in Bohmian
mechanics is discussed. It is emphasized that Bohmian mechanics
exactly reproduces the mean value and temporal and spatial
correlations obtained from the standard, that is the Copenhagen or
orthodox, formulation. The ontological characteristics of Bohmian
mechanics provide a description of measurements as another type
of interaction without the need for introducing the wave function
collapse. Several solved problems are presented at the end of the
chapter, giving additional mathematical support to some particular
issues. A detailed description of computational algorithms to obtain
Bohmian trajectories from the numerical solution of the Schro¨dinger
or the Hamilton-Jacobi equations are presented in an appendix. The
motivation of this chapter is twofold: first, as a didactic introduction
to Bohmian formalism, which is used in the subsequent chapters,
and second, as a self-contained summary for any newcomer
interested in using Bohmian mechanics in his or her daily research
activity.
