Bohmian mechanics with discrete operators

A deterministic and time reversible Bohmian mechanics for operators with continuous and discrete spectra is presented. Randomness enters only through initial conditions. Operators with discrete spectra are incorporated into Bohmian mechanics by associating with each operator a continuous variable in which a finite range of the continuous variable corresponds to the same discrete eigenvalue. In this way a deterministic and time reversible Bohmian mechanics can handle the creation and annihilation of particles. The formalism does not depend on the details of the Hamiltonian. Furthermore, many consistent choices, are available for. the dynamics. Examples are given and generalizations are discussed.