  The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian
random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre
RME), are applicable to following quantum statistical systems: nuclear systems,
molecular systems, condensed phase systems, disordered systems, and
two-dimensional electron systems (Wigner-Dyson electrostatic analogy). A family
of quantum anharmonic oscillators in one spatial dimension is studied and the
numerical investigation of their eigenenergies is presented. The statistical
properties of the calculated eigenenergies are compared with the theoretical
predictions inferred from the random matrix theory. Conclusions are derived.
