  Lower bound for the shape complexity measure of L\'opez-Ruiz-Mancini-Calbet
(LMC), $C_{LMC}$, is derived.
  Analytical relations for simple examples of the harmonic oscillator, the
hydrogen atom and two-electron 'entangled artificial' atom proposed by
Moshinsky are derived. Several numerical examples of the spherically confined
model systems are presented as the test cases. For the homogeneous potential,
$C_{LMC}$ is found to be independent of the parameters in the potential which
is not the case for the non-homogeneous potentials.
