Spectrum of Schrödinger Hamiltonian operator with singular inverted complex and Kratzer's molecular potentials in fractional dimensions

Singular potentials play a key role in the study of quantum properties of molecular interactions and in different branches of physics and quantum chemistry. They assist us to understand the structure of condensed matter and several biological dynamical systems as well as a number of chemical processes. Complex-potential models arise also in nuclear, atomic molecular physics and other fields, and are of special interest. Most of the studies done in the literature are based on the analysis of quantum systems with integer dimensions. However, the concept of fractional or non-integer dimensions has received recently much interest, since a number of quantum physics phenomena are accurately modelled in fractional dimensional spaces. In this paper, we determine the spectrum of the Schrödinger operator in fractional dimensions with an inverted complex singular potential and we solve the corresponding time-dependent wave equation for the case of a complex singular potential and a Kratzer's molecular potential, which has wide applications in solid-state physics and molecular physics. Several properties are analyzed and discussed accordingly.