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Series solution of a central potential problem with three-term recursion relation
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Series solution of a central potential problem with three-term recursion relation
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math-ph
math.MPquant-ph
keywords
coulombpotentialrecursionrelationseriessolutionsolvestates
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The series solution of the radial part of the Schr\"odinger equation for simultaneous coulomb and harmonic potential involves three-term recursion relation and is thus difficult to solve for bound states. We have suggested a simple method to solve for low lying states. Finite polynomial solutions exist only if the coulomb and oscillator potentials are nontrivially related.
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