Related papers: A systematic study on the exact solution of the po…
Using the method of $su(1,1)$ spectrum generating algebra, we analyze one dimensional Schroedinger equation with potential in the form ${C\over{x^2} + {D\over{x}}$ to obtain a class of potentials giving similar eigenvalues. By a group…
We discuss the explicit construction of the Schroedinger equations admitting a representation through some family of general polynomials. Almost all solvable quantum potentials are shown to be generated by this approach. Some generalization…
We consider a free particle,V(r)=0, with position-dependent mass m(r)=1/(1+zeta^2*r^2)^2 in the d-dimensional schrodinger equation. The effective potential turns out to be a generalized Poschl-Teller potential that admits exact solution.
The interest of quadratic algebras for position-dependent mass Schr\"odinger equations is highlighted by constructing spectrum generating algebras for a class of d-dimensional radial harmonic oscillators with $d \ge 2$ and a specific mass…
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…
The Schroedinger equation for position-dependent mass singular oscillators is solved by means of the factorization method and point transformations. These systems share their spectrum with the conventional singular oscillator. Ladder…
The differential realization of the potential group SO(2,2) is used. The spectrum-generating algebra for a kind of exactly solvable potentials endowed with position-dependent mass is constructed.
First order integrals of motion for Schr\"odinger equations with position dependent masses are classified. Seventeen classes of such equations with non-equivalent symmetries are specified. They include integrable, superintegrable and…
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…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
We analytically solve the position-dependent mass (PDM) 1D Schr\"odinger equation for a new class of hyperbolic potentials $V_q^p(x) = -V_0\frac{\sinh^px}{\cosh^qx}, \, p= -2, 0, \dots q$ [see C. A. Downing, J. Math. Phys. 54 072101 (2013)]…
A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under su(1,1) algebra can be brought back to the general Natanzon hypergeometric…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
Two exactly-solvable confined models of the completely positive oscillator-shaped quantum well are proposed. Exact solutions of the position-dependent mass Schr\"odinger equation corresponding to the proposed quantum well potentials are…
We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.
We outline a general method for obtaining exact solutions of Schr\"{o}dinger equations with a position dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that…
The non-relativistic Schrodinger equation with the linear and Coulomb potentials is solved numerically in configuration space using the relaxation method. The numerical method presented in this paper is a plain explicit Schrodinger solver…
Maximal kinematical invariance groups of $2d$ Schr\"odinger equation with a position dependent mass and arbitrary potential are classified. It is demonstrated that there exist seven classes of such equations possessing non-equivalent…