  Many-body states described by a Schr\"{o}dinger equation include states of
overlapping waves of non-vanishing interaction energies. These peculiar states
formed in many-body transitions remain in asymptotic regions, and lead a new
component to the transition probability. The probability is computed rigorously
following the von Neumann's fundamental principle of quantum mechanics with an
S-matrix that is defined with normalized functions, instead of plane waves.
That includes the intriguing correction term to the Fermi's golden rule, in
which a visible energy is smaller than the initial energy, and reveals
macroscopic quantum phenomena for light particles. Processes in Quantum
Electrodynamics are analyzed and the sizable corrections are found in the
dilute systems. The results suggest that these states play important roles in
natural phenomena, and the verification in laboratory would be possible with
recent advanced technology.
