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Approximate energy expressions for confining polynomial potentials

Institute of Physics, Sri Lanka
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  • Physics


Recently developed asymptotic energy expansion (AEE) method is applied to obtain asymptotic energy expansions (AEEs) of general polynomial potentials. These expansions contain coefficients of the polynomial potentials explicitly. The asymptotic expansions produce very accurate eigen energies. Recurrence relations derived here can be used to obtain asymptotic expansions of polynomial potentials of any degree. Energy eigen value expressions are presented for the 4th, 6th, 8th and 10th degree polynomial potentials. The expansions obtained with AEE method for polynomial potentials have resemblance with WKB expressions obtained by Bender et al1 for the potentials V(x) = xN (N even). doi:10.4038/sljp.v3i0.182 Sri Lankan Journal of Physics, Vol.3 (2002) 17-37

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