The lasting appeal of the ``next-to-harmonic" and ``first
unsolvable" quantum bound-state models with central polynomial
potentials derives from their broad phenomenological
applicability. For this reason one encounters numerous attempts at
construction of reliable interpolation/extrapolation closed
formulae for the energies, among which the most valuable ones
offer the approximative or strict lower and/or upper estimates.
The paper in question offers and discusses a number of new and/or
most updated formulae of this type which are mainly based on the
idea of sophisticated semiclassical approximation. Particular
attention is paid to the family of the two-term potentials of the
so called anharmonic oscillator.


MR2384005 Katatbeh, Qutaibeh D.; Hall, Richard L.; Saad, Nasser
Eigenvalue bounds for polynomial central potentials in $d$
dimensions. J. Phys. A 40 (2007), no. 44, 13431--13442. 81Q10
(35J10 47N50)