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The quantization method based on the quantum Hamiltonian Jacobi equation, isextended to two-dimensional non-separable but integrable Hamiltonians. It isshown that each wave function for those systems corresponds to a well-definedfamily of classical trajectories, enveloped by a caustic. The energyeigenvalues and the values of the wave functions on the caustic are obtained bysolving the 1-dim quantum Hamilton Jacobi equation of the caustic' arcs.Results are in good agreement with those obtained by usual methods.

Hamilton-Jacobi Approach to the Quantization of Classically Non-Separable but Integrable Two-Dimensional Systems: the Role of the Classical Caustics