Trajectory-based formalisms are an intuitively appealing way of
describing quantum processes because they allow the use of
"classical" concepts. Beginning at an introductory level suitable
for students, this two-volume monograph presents (1) the
fundamentals and (2) the applications of the trajectory description
of basic quantum processes. This first volume is focussed on the
classical and quantum background necessary to understand the
fundamentals of Bohmian mechanics, which can be considered the main
topic of this work. Extensions of the formalism to the fields of
open quantum systems and to optics are also proposed and discussed.
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