Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov
method and polynomial solutions of biconfluent Heun equation | Journal of Mathematical …

We present an asymmetric step–barrier potential for which the one-dimensional stationary
Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions …

Applicability of the extended Nikiforov–Uvarov method in order to obtain eigenstate
solutions of the radial Schrödinger equation in the presence of external magnetic field and …

Exact eigenstate solutions of Schrödinger equation for a generalized oscillator system that
includes, as special cases; ring shaped oscillator potential and isotropic harmonic oscillator …

In this paper, we state an algorithm that checks whether a given second-order linear
differential equation can be reduced to the tri-confluent Heun's equation. The algorithm …

We study in detail the relationship between the Tavis-Cummings Hamiltonian of quantum
optics and a family of quasi-exactly solvable Schrödinger equations. The connection …

With certain constraints on the parameters μ 4 and μ 2, it is known that the Schrödinger
equation with the sextic anharmonic oscillator potential V (r)= r 6+ μ 4 r 4+ μ 2 r 2 is quasi …

The analysis of many physical phenomena is reduced to the study of linear differential
equations with polynomial coefficients. The present work establishes the necessary and …

In the paper, the well-known quantum mechanical problem of a spin 1/2 particle in external
Coulomb potential, reduced to a system of two first-order differential equations, is studied …

Methods for solving the differential equation describing the wave functions of a polarizable
particle in the Coulomb potential are discussed. Relations between the coefficients under …