Spontaneous decay of level from spectral theory point of view

In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level due to interaction with continuum modes. Besides, atom makes a transition from upper lower one so probability find in state tends zero. this paper will be shown mathematical model single-photon approximation may predict another behavior generally. Namely, tend nonzero constant not pure finally. This effect spectrum complete Hamiltonian purely absolutely continuous and has discrete outside part. we corresponding invariant subspace, determining time evolution, when considered three dimensions have an eigenvalue. The appearance eigenvalue threshold character. If two always absent.