Precise analytical approximations of the eigenvalues of the decatic anharmonic potential
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2024
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Precise analytical approximations have been determined for the eigenvalues of the ground state of the decatic anharmonic potential x2+λx10 in the one-dimensional Schrodinger equation. The results have been found using the technique multipoint quasirational approximation (MPQA). With the new method, power and asymptotic expansions have been determined. The analytic function here obtained is derived connecting both expansions. The maximum relative error of the best analytical approximation here determined is 0.04. However, most of the relative errors for other values of λ, are smaller than 1% (less than 0.01).