Energies of the αx³+ βx⁴anharmonic oscillator calculated by using the hypervirial relations

Energies of oscillators with mixed quartic and sextic anharmonicities

“…This enables us to compare the results of the present calculations with those of various workers who have exploited different techniques for the extensive study of the oscillators with quartic [1,4,7,[23][24][25][26][27][28][29][30][31][32][33][34][35] and sextic [8, 24-26, 33, 36] anharmonicities.…”

“…The only input in the algorithm of this approach is the unperturbed energy of the corresponding state of the system. This method has been used to calculate energy values for the quartic anharmonic oscillator [3] and the doubly anharmonic oscillator with cubic and quartic anharmonicities [4] up to different orders in the perturbation parameter. But Lai and Madan [4] found that the results obtained in the case of the latter are correct (and hence reliable) only for small values of the perturbation parameter (2) and the quantum number (n).…”

An eigenvalue moment method analysis of theV(x) = [ω2/2]x2+ αx3+ βx4anharmonic oscillator

“…The focus of this work is the application of the EMM technique to the V(x) = [~o2/2]x 2 + ~x 3 + fix 4 studied by Lai and Madan [11] and Fernandez et al [12]. By so doing, we can contrast the effectiveness of all three methods.…”

Perturbative calculation of energy levels for coupled oscillators using the adiabatic approximation

“…This procedure has been applied successfully to several quantum problems [21][22][23][24][25]. Our purpose, in the present paper, is to develop the hypervirial treatment for obtaining the adiabatic eigenvalues corresponding to a system of coupled oscillators.…”