  A time dependent variational principle is used to dequantize a second order
quadrupole boson Hamiltonian. The classical equations for the generalized
coordinate and the constraint for angular momentum are quantized and then
analytically solved. A generalized Holmberg-Lipas formula for energies is
obtained. A similar $J(J+1)$ dependence is provided by the coherent state model
(CSM) in the large deformation regime, by using an expansion in powers of $1/x$
for energies, with $x$ denoting a deformation parameter squared. A simple
compact expression is also possible for the near vibrational regime. These
three expressions have been used for 44 nuclei covering regions characterized
by different dynamic symmetries or in other words belonging to the all known
nuclear phases. Nuclei satisfying the specific symmetries of the critical point
in the phase transitions $O(6)\to SU(3)$, $SU(5)\to SU(3)$ have been also
considered. The agreement between the results and the corresponding
experimental data is very good. This is reflected in very small r.m.s. values
of deviations.
