Quantization of time-dependent singular potential systems in one-dimension by using the Nikiforov-Uvarov method

Abstract

The technique for quantizing simple static systems can be extended to more generalized systems that involve time-dependent parameters. In this work, a particle with linearly increasing mass that is bound by a time-dependent singular potential, which is composed of an inverse quadratic potential and a Coulomb-like potential, is quantized by using the Nikiforov-Uvarov method together with the invariant operator method and the unitary transformation method. The Nikiforov-Uvarov method is an alternative method for solving the Schrödinger equation on the basis of a particular mathematical technique that reduces second-order differential equations to generalized hypergeometric ones. The exact wave functions of the system are identified, and their properties are addressed in detail.

Quantization of time-dependent non-central singular potential systems in three dimensions by using the Nikiforov-Uvarov method

“…By applying the same method of Ref. [9] when solving Eq. (13), which is based on the NU method, we easily derive the radial wave function such that…”

“…The required functions needed for unfolding the corresponding theory of NU for this case are as follows (see Appendix A of Ref. [9]):…”

“…Let us use the NU method [9,[15][16][17], which is useful for solving the solution of this equation. Usually, the NU method starts from the following equation [9]:…”

“…In a previous work [9], we investigated quantum solutions of the one-dimensional problem of a linearly increasing mass system subjected to a timedependent inverse quadratic potential and the Coulomb potential. Three-dimensional problems of quantum solutions for a non-central potential system with a timedependent mass will be studied in this work.…”

“…A quadratic invariant operator of the system will be introduced, and it will be transformed to a simple form by means of the unitary transformation method. Quantum solutions in the transformed system will be derived using the Nikiforov-Uvarov (NU) method [9,[15][16][17]. This method is a mathematical manipulation for solving second-order linear diffierential equations by reducing the original equation to a hypergeometric type.…”