The anharmonic oscillator: perturbation series for cubic and quartic energy distortion

Non-perturbative Description of Quantum Systems

“…At the same time, the coefficients C nk depend on the choice of the parameter !, which defines the basis set of the states jn; !i in the exact vector j« n i. The results shown in the Table 2.9 demonstrate that for certain values of a high accuracy of results is obtained using fast numerical calculations by formulas (2.126) in comparison with the results obtained by other authors using complex numerical methods (see, e.g., [65]). …”

Perturbation series for transition moments of anharmonic oscillators

“…For a general Ax2" perturbation a BASIC computer program has been produced which calculates renormalised perturbation series for any (mlxl n) to arbitrary order. With the selection (Y = p = 1 in (3) and ( 5 ) and for a quartic perturbation ( v = 2), the energy perturbation coefficients required by the fourth-order (01x1 1) moment calculation are given by Drummond (1981) and are shown in table 2. The energy coefficients can also be calculated with the microcomputer program of Killingbeck (1983).…”

A resurgence analysis for cubic and quartic anharmonic potentials

“…The usual Rayleigh-Schrödinger perturbative expansion of the ground state energy for this potential yields the following expansion [20,21] E ground (g) =…”

“…The Rayleigh-Schrödinger perturbation theory yields the following energy expansion for the ground state energy [18,21]…”