---
abstract: 'The time reversal and irreversibility in conventional quantum mechanics are compared with those of the rigged Hilbert space quantum mechanics. We discuss the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged Hilbert space case admits a new kind of irreversibility which does not appear in the conventional case. The origin of this irreversibility can be traced back to different initial-boundary conditions for the states and observables. It is shown that this irreversibility does not contradict the experimentally tested consequences of the time-reversal invariance of the conventional case but instead we have to introduce a new time reversal operator.'
author:
- |
    A. Bohm\
    [*Department of Physics, University of Texas, Austin, TX 78712, U.S.A*]{}\
- |
    P. Kielanowski\
    [*Institute of Theoretical Physics, Warsaw University, Poland*]{}\
    [*and*]{}\
    [*Departamento de Física, CINVESTAV del IPN, Mexico*]{}
title: 'Time-Reversal and Irreversibility[^1]'
---

Introduction
============

Irreversibility in the title refers to intrinsic irreversibility for quantum physical systems on the microphysical level; this means there exist microphysical “states” $\psi$ whose time evolution (generated by an essentially self-adjoint semibounded Hamiltonian $H$) $\psi(t)=\mbox{``e}^{-iHt/\hbar}\mbox{''}\psi(0)$ has a preferred direction, $t\geq0$, [@R1]. Time reversal in the title refers to the existence of an operator $A_T$ which 