where | e ; 0 ⟩ ⟩ and a ( t ) are the atomic excited state-electromagnetic vacuum wavefunction and its probability amplitude, | g ; 1 k s ⟩ ⟩ and b k s ( t ) are the ground state atom with a single photon (of mode k s ) wavefunction and its probability amplitude, ω ω 0 is the atomic transition frequency, and ω ω k = c | k | is the frequency of the photon. The sum is over k and s , which are the wavenumber and polarization of the emitted photon, respectively. As mentioned above, the emitted photon has a chance to be emitted with different wavenumbers and polarizations, and the resulting wavefunction is a superposition of these possibilities. To calculate the probability of the atom at the ground state ( | b ( t ) | 2 ), one needs to solve the time evolution of the wavefunction with an appropriate Hamiltonian. To solve for the transition amplitude, one needs to average over (integrate over) all the vacuum modes, since one must consider the probabilities that the emitted photon occupies various parts of phase space equally. The "spontaneously" emitted photon has infinite different modes to propagate into, thus the probability of the atom re-absorbing the photon and returning to the original state is negligible, making the atomic decay practically irreversible. Such irreversible time evolution of the atom-vacuum system is responsible for the apparent spontaneous decay of an excited atom. If one were to keep track of all the vacuum modes, the combined atom-vacuum system would undergo unitary time evolution, making the decay process reversible. Cavity quantum electrodynamics is one such system where the vacuum modes are modified resulting in the reversible decay process, see also Quantum revival. The theory of the spontaneous emission under the QED framework was first calculated by Victor Weisskopf and Eugene Wigner in 1930 in a landmark paper. The Weisskopf-Wigner calculation remains the standard approach to spontaneous radiation emission in atomic and molecular physics. Dirac had also developed the same calculation a couple of years prior to the paper by Wigner and Weisskopf.