# Explicit energy expansion for general odd-degree polynomial potentials

@article{Nanayakkara2013ExplicitEE, title={Explicit energy expansion for general odd-degree polynomial potentials}, author={Asiri Nanayakkara and Thilagarajah Mathanaranjan}, journal={Physica Scripta}, year={2013}, volume={88} }

In this paper we derive an almost explicit analytic formula for asymptotic eigenenergy expansion of arbitrary odd-degree polynomial potentials of the form V (x) = (ix)2N+1 + β1x2N + β2x2N−1 + ··· + β2Nx, where β′k are real or complex for 1 ⩽ k ⩽ 2N. The formula can be used to find semiclassical analytic expressions for eigenenergies up to any order, very efficiently. Each term of the expansion is given explicitly as a multinomial of the parameters β1,β2… and β2N of the potential. Unlike in the…

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