We construct the solution of the quantum wave equation as a bilinear form which can be expanded over Wick polynomials of the free -field, and where is defined as the normal ordered product with respect to the free -field. The constructed solution is correctly defined as a bilinear form on where is a dense linear subspace in the Fock space of the free -field. On the diagonal of the Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.
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