 For simplicity, we restrict attention to the possible states of the system that are spanned by this set. We posit a Hamiltonian that has the effect of leaving |0⟩ invariant; of creating |1⟩ and destroying |2⟩; of creating |2⟩ and destroying |3⟩; and so on. Norton then solved the differential form of the Schrödinger equation for this interaction and argued that it admits solutions in which all of the nodes in the infinite lattice start in their ground state, but all become spontaneously excited in finite time.