Approximate Solution of GCF PDM Schrodinger Equation for a Symmetrical Modified Poschl-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 Phi generated by the fractional conformable function phi. By the new definition, the usual Laplace transform and the rho-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) Schrodinger equation for a symmetrical modified Poschl-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 Schrodinger 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 alpha, 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 alpha and mass for diatomic molecules H-2, LiH, and HCl.