On the αx2+ βx4interaction

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Abstract
By applying the Laplace transform method the authors obtain a class of exact solutions for the Schrodinger equation with the potential V(x)= alpha x2+ beta x4, x>0, alpha >or=0, beta <0, the corresponding energy spectrum being continuous. A particular feature of these eigen-solutions is that they may not be accessible to perturbation theory. The properties of the solutions obtained are investigated and their relation to the case where x<or=0 is included is discussed.