Related papers: Inter-Relations of Solvable Potentials
All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on $\hbar$, and their $\hbar$-dependent extensions. The former group…
The exactly solvable Schr\"{o}dinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the…
A recurrence relation of Riccati-type differential equations known in supersymmetric quantum mechanics is investigated to find exactly solvable potentials. Taking some simple {\it ans\"atze}, we find new classes of solvable potentials as…
A new class of quasi exactly solvable potentials with a variable mass in the Schroedinger equation is presented. We have derived a general expression for the potentials also including Natanzon confluent potentials. The general solution of…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
We show that the Natanzon family of potentials is necessarily dropped into a restricted set of distinct potentials involving a fewer number of independent parameters if the potential term in the Schr\"odinger equation is proportional to an…
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the…
A new family of solvable potentials related to the Schroedinger-Riccati equation has been investigated. This one-dimensional potential family depends on parameters and is restricted to the real interval. It is shown that this potential…
The present article discusses the connection between exactly-solvable Schrodinger equations and the Liouville transformation. This transformation yields a large class of exactly-solvable potentials, including the exactly-solvable potentials…
An algebraic method of constructing the confluent Natanzon potentials endowed with position-dependent mass is presented. This is possible by identifying the scaling resolvent operator (Green's function) to nonrelativistic position-dependent…
We obtained a new class of exactly-solvable potentials by means of the hypergeometric equation for Schrodinger equation, which different from the exactly-solvable potentials introduced by Bose and Natanzon. Using the new class of solvable…
The potentials $V (v)$ in the nonrelativistic (relativistic) nucleon-nucleon (NN) Schroedingerequation are related by a quadratic equation. That equation is numerically solved, thus providing phase equivalent v- potentials related for…
Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…
An analytical relation between center of mass momenta in a nonrelativistic and a relativistic two-nucleon Schr\"odinger equation is proposed which allows to analytically rewrite the two Schr\"odinger equations into each other. As a…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…
The recently introduced scheme [20,21] is extended to propose an algebraic non-perturbative approach for the analytical treatment of Schr\"odinger equations with non-solvable potentials involving an exactly solvable potential form together…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…