  In quantum physics, disturbance due to a measurement is not negligible. This
requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to
be considered differently from a time continuum of experimenter's clock $T$ on
which physical events are recorded. It will be shown that $t$ represents an
ensemble of time intervals on $T$ during which a microsystem travels
undisturbed. In particular $t=0$ represents the ensemble of preparation events
that we refer to as the ensemble of beginnings of time. This restricts $t$ to
be $0\leq t<\infty$. But such a time evolution of quantum states cannot be
achieved in the Hilbert space $L^2$ functions because due to the Stone-von
Neumann theorem this time evolution is given by the unitary group with $t$
extending $-\infty<t<\infty$. Hence one needs solutions of the Schr\"odinger
(and Heisenberg) equation under time asymmetric boundary condition in which
only the semigroup time evolution is allowed. This boundary condition is
fulfilled by the energy wave functions for quantum states (and as well as for
observables) which are smooth Hardy function satisfying the Hilbert transform,
called the dispersion relation in physics.
