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We present perturbative energy eigenvalues (up to second order) of Coulomb-and harmonic oscillator-type fields within a perturbation scheme. We have therequired unperturbed eigenvalues ($E_{n}^{(0)}$) analytically obtained by usingsimilarities between the expressions obtained from unperturbed Hamiltonian(s)for two fields and obtained from the ones for one-dimensional generalized Morsefield. We use the Langer transformation for this aim. We need the diagonal andnon-diagonal matrix elements of unperturbed and perturbed Hamiltonians to getenergy eigenvalues perturbatively, which are obtained with help of somerecursion identities or some integrals of generalized Laguerre polynomialshaving analytical results.

the european physical journal plus

Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type  Potentials from One-Dimensional Generalized Morse Potential: Perturbative  Analyse based on Generalized Laguerre Polynomials