Abstract
Schrodinger equation for a polynomial potential with the highest order term having an even power and a positive coefficient is solved for high eigenvalues En in two different ways after Liouville transformation, (a) converting the differential equation into integral equation and solving it iteratively and (b) by the WKB method. While the series solution in powers of 1/En from (b) is known to diverge, we show that the one from (a) converges. We show then that asymptotic re‐expansion of the convergent series from (a) agrees with the divergent series from (b). Actually, we have been able to show the agreement only up to order (1/En)5, but we believe that it holds to all orders. If this is true, the divergent WKB series can be reorganized into a convergent series, which is in fact obtained by the method of iteration (a).
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