G. Ovando

On the equivalence of radial potential models for diatomic molecules

AbstractIn this work, we show that various quantum interaction radial potential models used for describing diatomic molecules are particular cases of an exactly solvable multiparameter exponential-type potential. This feature is exploited to find the conditions that potentials should fulfill to be considered as equivalent. As an example of the usefulness of the proposal, the obtained requirements are applied to some of the most common diatomic potential models. Specifically, we have shown the equivalence among the radial potentials of Manning–Rosen, Deng–Fang, Schiöberg, Badawi–Bessis–Bessis, Tietz, Wie, Sun, the negative of the Williams–Poulios and the Möbius square potentials. The proposal to obtain equivalent radial potentials is general and can be directly applied to other interaction models as well as in the study of relativistic molecular physics.

A Lanczos Potential for Plane Gravitational Waves

We exhibit explicitly a Lanczos generator for the conformal tensor associated with plane gravitational waves.

The Darboux Transform Applied to Schrödinger Equations with a Position-Dependent Mass

Essentially, the Darboux proposition is based on the covariance properties of ordinary and partial differential equations with respect to a gauge transformation in the special case of second order differential equations of the Sturm- Liouville type. In this work, the one-dimensional Schrodinger equation with a position-dependent mass (SEPDM) is transformed into a Schrodinger-like equation with a position-independent mass (SLEPIM) for an effective potential which incorporates the spatially dependent mass. Therefore, taking advantage of the similarity between the SLEPIM and the Sturm-Liouville differential equation it is shown the application of the Darboux transform to the SEPDM problem.

Kratzer potential algebraic representation and matrix elements recurrence formulae

Generalized recurrence relations for the calculation of multipole matrix elements for Kratzer potential wave functions are obtained operationally. These formulas have been determined by using a non-analytical procedure based on the algebraic representation of the Kratzer eigenfunctions along with the usual ladder properties and commutation relations. For that, the creation and annihilation operators are adequately derived by means of an alternative approach to the factorization method and the exact expressions for matrix elements are achieved with the aid of a relationship between the ladder operators associated with the bra and theket. The proposed algebraic approach as well as the formulas for the calculation of matrix elements thus derived are quite simple and direct when compared with other alternative expressions already obtained analytically or pseudo-algebraically by means of the hypervirial theorem commutator algebra.