the annihilation operator of the field, , where and are frequency parameters used to simplify equations. Now that the dynamics of the field with respect to the states of the atom has been described, the mechanism through which photons are released from the atom as the electron falls from the excited state to the ground state, Spontaneous Emission, can be examined. Spontaneous emission is when an excited electron arbitrarily decays to the ground state emitting a photon. As the electromagnetic field is coupled to the state of the atom, and the atom can only absorb a single photon before having to decay, the most basic case then is if the field only contains a single photon. Thus spontaneous decay occurs when the excited state of the atom emits a photon back into the vacuum Fock state of the field . During this process the decay of the expectation values of the above operators follow the following relations , . So the atom decays exponentially and the atomic dipole moment shall oscillate. The dipole moment oscillates due to the Lamb shift, which is a shift in the energy levels of the atom due to fluctuations of the field. It is imperative, however, to look at fluorescence in the presence of a field with many photons, as this is a much more general case. This is the case in which the atom goes through many excitation cycles. In this case the exciting field emitted from the laser is in the form of coherent states . This allows for the operators which comprise the field to act on the coherent state and thus be replaced with eigenvalues. Thus we can simplify the equations by allowing operators to be turned into constants. The field can then be described much more classically than a quantized field normally would be able to. As a result, we are able to find the expectation value of the electric field for the retarded time. , where is the angle between and . There are two general types of excitations produced by fields. The first is one that dies out as , while the other one reaches a state in which it eventually reaches a constant amplitude, thus . Here is a real normalization constant, is a real phase factor, and is a unit vector which indicates the direction of the excitation. Thus as , then . As is the