Exact analytic solutions generated from stipulated Morse and trigonometric Scarf potentials

Abstract

The extended transformation method has been applied to the exactly solvable stipulated Morse potential and trigonometric Scarf potential, to generate a set of exactly solvable quantum systems (QSs) in any chosen dimension. Bound state solutions of the exactly solvable potentials are given. The generated QSs are generally of Sturmian form. We also report a system case-specific regrouping technique to convert a Sturmian QS to a normal QS. A second-order application of the transformation method is given. The normalizability of the generated QSs is generally given in Sturmian form.

A Transformation Method to Construct Family of Exactly Solvable Potentials in Quantum Mechanics

“…(ii) Continuing the procedure to construct exactly solvable quantum system we consider second term g ′2 g of expression (14) to be constant independent of r. i.e.,…”

“…This is because, despite the intrinsic interest of the exactly solvable systems, these solutions can be used to get better approximated solutions for potentials which are physically interesting. To enhance the set of exactly solvable potentials, we follow a simple and compact transformation method [10,[13][14][15][16] which comprises of a co-ordinate transformation supplemented by a functional transformation. By applying this method, we transform the second order ordinary differential equation satisfied by special functions to standard Schrodinger equation in arbitrary D-dimensional Euclidean space and thus try to construct as many exactly solvable potentials as possible.…”

Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

“…Thus the energy levels depend on the quantum numbers n, l and . (41) Pseudospin symmetry case For pseudospin symmetry we must choose Σ as constant. This time ∆ is assumed to be given by…”

“…We will study Pöschl-Teller potential [31][32][33][34][35][36][37][38]. Morse Potential [39][40][41], Mie potential [42][43][44][45][46][47][48][49], Pesudoharmonic potential and Kratzer-Fues Potential [50,51] This paper is organized as follows. In section 2, the Dirac equation is solved for the scalar, vector plus a tensor interaction.…”

New Method for Mapping of Exact Analytic S-wave Solutions for Regenerated Central Hyperbolic Potentials

“…Again, the extended transformation (ET) [6] is applied successfully by Ahmed et al and others for the generation of exactly solvable central potentials (ESCPs) in an Euclidean space of any desired dimension from already known ESCPs (power law and non-power law) [7][8][9][10][11][12]. The ET includes a coordinate transformation (CT) required to modify the spatial character of an already known ESCP to generate a new ESCP and a functional transformation (FT) for manipulation of the dimensionality of the space to which the known QS gets transformed.…”