I'm reading Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" and I'm up to Section 6.2 which is called "A toy model for electrons in an atom". He has a nonrelativistic particle of mass M and a scalar field with quanta of mass m and the state space for the particle is L^2(T^3) for a 3-torus T^3 and the state space for the field is the Boson Fock space over L^2(T^3), and he describes the Hamiltonian for the particle, for the field, and for the interactions, and then starts calculating the expected time interval for the emission of a field quantum. So you start with the state corresponding to the particle in energy state n and no field quanta present, then apply the time evolution operator U(t) for some specific t>0, then apply the linear functional corresponding to the state where the particle is in state m and there is one field quantum present with momentum p, and the modulus squared of the result gives you the transition probability. I am trying to understand better how this actually links with actual experimental results. Can we make sense of the idea of just staring constantly at a hydrogen atom and waiting to see if anything happens, is that an experiment that is actually feasible to do? I vaguely remember reading somewhere that if you do that then emission of a photon will not happen. Am I wrong about that?