Minimal irreversible quantum mechanics: Pure-state formalism

Abstract

It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decomposition, with eigenvectors corresponding to unstable states that vanish when $t\ensuremath{\rightarrow}\ensuremath{\infty}.$ These Gamov vectors have zero norm, in such a way that the norm and the energy of the physical states remain constant. The evolution operator has no inverse, showing that we are really dealing with a time-asymmetric theory. Using the Friedrichs model, reasonable physical results are obtained, e.g., the remnant of an unstable decaying state reappears, in the continuous spectrum of the model, with its primitive energy.