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The non-relativistic analytic solutions of a quantum mechanical system have been calculated for the case of pseudoharmonic potential by using the Whittaker functions approach. A diatomic quantum system is placed in a Pseudoharmonic potential and perturbed by an external magnetic field. The resulting Schrodinger’s equation has been solved exactly to obtain the analytic expressions of vibrational energy levels and associated wave functions. In this work, we have compared the results of six diatomic molecules with those available in the literature.

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The number of quantum systems for which the stationary Schrodinger equation is exactly solvable is very limited. These systems constitute the basic elements of the quantum theory of perturbation. The exact polynomial solutions for real quantum potential systems provided by the use of Lagrange interpolation allows further development of the quantum perturbation theory. In fact, the first order of correction for the value of the energy appears to be sufficient since the chosen perturbation Hamiltonian is very small or even negligible compared to the main Hamiltonian. Here, we use the perturbation theory to derive polynomial solutions, and we then find that our approximated results agree very well with previous published or numerically achieved ones. We believe that this study is an operational tool for the verification and improvement of numerical and approximate methods.