Abstract
Asymptotic energy expansion method is extended for polynomial potentials having rational powers. New types of recurrence relations are derived for the potentials of the form V (x) = x2n/m + b1xn1/m1 + b2xn2/m2 + … + bNxnN/mN where n, m, n1, m1, …, nN, mN are positive integers while coefficients bk ∈ ℂ. As in the case of even degree polynomial potentials with integer powers, all the integrals in the expansion can be evaluated analytically in terms of Γ functions. With the help of two examples, we demonstrate the usefulness of these expansions in getting analytic insight into the quantum systems having rational power polynomial potentials.
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