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The solution for the large-radius Fr\"{o}hlich polaron in the Schr\"{o}dingerrepresentation of the quantum theory is constructed in the entire range ofvariation of the coupling constant. The energy and the effective mass of thepolaron are calculated by simple algebraic transformations and are analogous tothe results found by Feynman on the basis of the variational principle for thepath-integrals of this system. It allows us to solve the long-lived problem ofthe inequalities of the functional and operator approaches for the polaronproblem. The developed method is important for other models of particle-fieldinteraction including those ones for which the standard perturbation theory isdivergent.

All-coupling solution for the continuous polaron problem in the Schr\"{o}dinger representation