An alternative formulation of the WKB approximation in quantum mechanics

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An expansion of Schrodinger's theory in powers of h is presented. It has the property that the standard WKB results, together with the Bohr-Sommerfeld quantization condition are obtainable by a zeroth-order perturbation in h, rather than by a first-order one (in contrast with the usual expansion methods). It also makes the connection between the (classical) Hamilton-Jacobi equation and the WKB approximation more transparent.