When \(A_f\) is elevated but not emitted, the particle remains in a elevated state (not an excited state denoted by \(a_f\) but an elevated state denoted by \(A_f\neq 0\)) until next photon impact drives \(A_f\) beyond the emission threshold and a photon is emitted. As highlighted in the post "Pop Now, Pop Later" dated 06 Oct 2017, it is possible that this photon is emitted when the particle is at the excited energy state (\(a_i\)), or on the particle's return to the lower energy stated at \(a_f\).
But the maximum speed is light speed. The residue energy that remains with the particle results in the wave amplitude not being zero; at \(a_i\), \(A_i\neq 0\) or at \(a_f\), \(A_f\neq 0\). In either case, the particle is in an elevated state. The particle is still restricted to quantized energy states, \(a_n\), but its amplitude \(A_n\) allows for a spread of energy and a mechanism for state transitions.
How does this spread of energy manifest itself?
