Short-range oscillators in power-series picture
نویسنده
چکیده
Abstract The class of short-range potentials V [M (x) = ∑M m=2(fm + gm sinh x)/ cosh m x is considered as an asymptotically vanishing phenomenological alternative to the popular anharmonic long-range V (x) = ∑N n=2 hnx . We propose a method which parallels the analytic Hill-Taylor description of anharmonic oscillators and represents all the wave functions ψ (x) non-numerically, in terms of certain infinite hypergeometriclike series. In this way the well known exact M = 2 solution is generalized to any M > 2.
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