  In this treatise I introduce the time dependent Generalized Born's Rule for
the probabilities of quantum events, including conditional and consecutive
probabilities, as the unique fundamental time evolution equation of quantum
theory. Then these probabilities, computed from states and events, are to be
compared with relative frequencies of observations. Schrodinger's equation
still is valid in one model of the axioms of quantum theory, which I call the
Schrodinger model. However, the role of Schrodinger's equation is auxiliary,
since it serves to help compute the continuous temporal evolution of the
probabilities given by the Generalized Born's Rule. In other models, such as
the Heisenberg model, the auxiliary equations are quite different, but the
Generalized Born's Rule is the same formula (covariance) and gives the same
results (invariance). Also some aspects of the Schrodinger model are not found
in the isomorphic Heisenberg model, and they therefore do not have any physical
significance. One example of this is the infamous collapse of the quantum
state. Other quantum phenomena, such as entanglement, are easy to analyze in
terms of the Generalized Born's Rule without any reference to the unnecessary
concept of collapse. Finally, this leads to the possibility of quantum theory
with other sorts of auxiliary equations instead of Schrodinger's equation, and
examples of this are given. Throughout this treatise the leit motif is the
central importance of quantum probability and most especially of the
simplifying role of the time dependent Generalized Born's Rule in quantum
theory.
