The problem of the spontaneous emission from a single excited two-level atom in the presence of N unexcited similar atoms is discussed. A formalism is presented for evaluation of the time-development operator (and thus the density matrix) which has certain desirable features for time-dependent problems in the area, e.g. of atom-field interactions, when the off-diagonal elements are large compared to the diagonal elements of the Hamiltonian. By use of this formalism, it is shown that the spontaneous emission from a single atom is often drastically altered in the presence of unexcited atoms with similar resonances. When the number of atoms present becomes very large relative to the number of modes of the electromagnetic field, the excited atom becomes trapped in its excited state. >