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Computations of energy levels, expectation values of various powers of internuclear separation, and Franck–Condon factors for molecular potentials have been carried out within the framework of shifted large‐N technique. In contrast to other perturbative as well as semiclassical calculations, we obtain compact analytic expressions for these quantities. For illustration, our predicted results for perturbed Kratzer potential are compared with those derived by numerical integration. The method gives quite accurate results for a wide range of rovibrational quantum numbers. Further possible applications, in particular, to Morse oscillators are finally discussed.

An expression is derived for the sixth nonzero term in the WKBJ approximation. The six‐term WKBJ approximation is applied to calculate the eigenvalues for the potential V(x) = 1/2 kx2+ax4, k≳0 and a≳0. At low values of λ[ = ah//( μk3)1/2], the calculated results are in excellent agreement, to 15 significant figures, with those of Banerjee et al. for all quantum numbers. At medium and high values of λ, the calculated results are poor at low quantum numbers, but improve rapidly as n increases. A 15‐significant‐figure accuracy is achieved at n = 10 for λ = 0.05, and at about n = 15 for λ = 20 000. For λ = 0.5, eigenvalues are calculated to 20 significant figures and an argument is presented to show that by n = 50, the calculated value is correct to 19 significant figures. The accuracy further improves at higher quantum numbers.

The Drickamer–Franck–Slichter model for the effects of high pressure on electronic spectra is reformulated by incorporating the Kratzer–Fues potential to allow for anharmonicity. The configuration‐coordinate parameters for the ground and excited states are shown to be readily derivable from the experimental data. The proposed model is applied to six cases for which experimental data are available.

Eigenvalues are determined for the plane pendulum problem by the WKBJ method in one‐ and four‐term approximations, and the results are compared. It is found that at high quantum numbers, the four‐term WKBJ approximation can yield eigenvalues of eight‐significant‐figure accuracy, but for low quantum numbers the results continue to be poor.

An expression is derived for the five‐term WKBJ approximation.An expression is derived for the five‐term WKBJ approximation.

By a combination of analytical and numerical methods, it is determined that the critical screening length for two particles interacting through an attractive static screened Coulomb potential lies between 0.8399032a0 and 0.8399039a0, where a0 is the Bohr radius.