Extending the stationary quantum mechanics of being to a nonstationary quantum theory of becoming and decaying (Q1381873)

A formulation of quantum mechanics using the mathematics of a rigged Hilbert space or the Gel'fand triplet (RHS) in place of the conventional theory in Hilbert space is dealt with. This RHS formulation provides a correct way to describe Dirac's ket vectors of exponential growth and decay, the Gamow vectors. It is shown how selfadjoint operators may have complex eigenvalues. Relations are given to the Gel'fand-Maurin theorem to make the Dirac formalism of quantum mechanics rigorous. Some of the arrows of time in classical physics are presented. Irreversibility on the microphysical level is discussed. The general quantum mechanical arrow of time from the preparation to the registration is formulated. Both von Neumann's Hilbert space formalism and the RHS formalism can be justified from the foundations of quantum mechanics.