For a densely defined self-adjoint operator H in Hilbert space F the operator exp(−itH) is the evolution operator for the Schrödinger equation iψThe space F here is the space of wave functions ψ defined on an abstract space Q, the configuration space of a quantum system, and H is the Hamiltonian of the system. In this paper the operator exp(−itH) for all real values of t is expressed in terms of the family of self-adjoint bounded operators S(t), t ≥ 0, which is Chernoff-tangent to the operator −H. One can take S(t) = exp(−tH), or use other, simple families S that are listed in the paper. The main theorem is proven on the level of semigroups of bounded operators in F so it can be used in a wider context due to its generality. Two examples of application are provided.
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