Approximate Solution of GCF PDM Schrödinger Equation for a Symmetrical Modified Pöschl–Teller Potential by GCF Laplace Transform Method

In this paper, we introduce a new definition of the general conformable fractional (GCF) Laplace transform with respect to the function Φ generated by the fractional conformable
function ϕ. By the new definition, the usual Laplace transform and the − Laplace transform are special cases of the GCF Laplace transform. We prove several important properties of these GCF Laplace transforms. In addition, we also define the GCF cylindrical coordinates system and derive the GCF Laplace operator on these coordinates. Furthermore, we study the approximate solution of the GCF position-dependent mass (PDM) Schrödinger equation for a symmetrical modified Pöschl-Teller potential in the GCF cylindrical coordinate system by using the GCF Laplace transform method. The GCF radial wave function and GCF energy eigenvalue are obtained from the approximate solution of the GCF Schrödinger equation. The behavior of the bound state conformable fractional energy levels was demonstrated and analyzed by using the computational method for various
values of the order of conformable fractionality, quantum number, and mass of the molecule. Moreover, the maximum conformable fractional energy-eigenvalue is obtained
with respect to the influence of the order of conformable fractionality and mass for diatomic molecules H
2 , LiH, and HCl.