Summary: For a densely defined self-adjoint operator \(\mathcal{H}\) in Hilbert space \(\mathcal{F}\) the operator \(\exp (- i t \mathcal{H})\) is the evolution operator for the Schrödinger equation \(i \psi_t^\prime = \mathcal{H} \psi\), i.e. if \(\psi(0, x) = \psi_0(x)\) then \(\psi(t, x) = (\exp (- i t \mathcal{H}) \psi_0)(x)\) for \(x \in Q\). The space \(\mathcal{F}\) here is the space of wave functions \(\psi\) defined on an abstract space \(Q\), the configuration space of a quantum system, and \(\mathcal{H}\) is the Hamiltonian of the system. In this paper the operator \(\exp (- i t \mathcal{H})\) for all real values of \(t\) is expressed in terms of the family of self-adjoint bounded operators \(S(t)\), \(t \geq 0\), which is Chernoff-tangent to the operator \(- \mathcal{H}\). One can take \(S(t) = \exp (- t \mathcal{H})\), 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 \(\mathcal{F}\) so it can be used in a wider context due to its generality. Two examples of application are provided.