Variational studies employing the basis functions of the quantal particle-in-a-box model are shown to lead to accurate estimates of eigenvalues, various expectation values and eigenfunctions of the stationary anharmonic oscillator problem. Calculations involve bothzx^2α and (x²⁺zx^2α)-type oscillators, withα=2, 3 and 4, both in weak and strong coupling regime. Apart from its recommendable computational simplicity, convergence of the present recipe has also been demonstrated to be quite fast. Results for the first ten states are reported. A few goodness tests for the approximate wavefunctions and consistency requirements for some properties are also performed.

Some problems associated with the use of the maximum entropy principle, namely, (i) possible divergence of the series that is exponentiated, (ii) input-dependent asymptotic behaviour of the density function resulting from the truncation of the said series, and (iii) non-vanishing of the density function at the boundaries of a finite domain are pointed out. Prescriptions for remedying the aforesaid problems are put forward. Pilot calculations involving the ground quantum eigenenergy states of the quartic oscillator, the particle-in-a-box model, and the classical Maxwellian speed and energy distributions lend credence to our approach.