Abstract
The usual second harmonic generation effective Hamiltonian is shown to be equivalent to a one-dimensional Schrodinger operator with a sextic polynomial potential. This operator belongs to the class of quasi-exactly solvable models, for which a finite number of eigenvalues and eigenvectors can be determined exactly. A Jeffreys-Wentzel-Kramers-Brillouin analysis provides accurate asymptotic expansions for these eigenvalues in the limit of large unperturbed energies.
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