Introducción

Quasi-exactly solvable relativistic soft-core Coulomb models

“…Let us remark at this point that the existence of a underlying Lie algebraic structure in a differential equation is only a sufficient condition for the differential equation to be quasi-exactly solvable. In fact there are more general (than the Lie-algebraically based) differential equations which do not possess a underlying Lie algebraic structure but are nevertheless quasi-exactly solvable (i.e have exact polynomial solutions ) [29,40].…”

Rational extension and Jacobi-type X m solutions of a quantum nonlinear oscillator

“…Observe that equation (36) has more solutions, but they all lead to positive λ, which is not allowed due to our standing assumption λ < 0. In the last step we consider the interior of D λ , applicable results for which in [6] give the restrictions stated in the second line of (23). After incorporation of the settings (16) for a and b and their evaluation, we obtain that the denominator of (34) does not have any zeros in D λ , if and only if the following condition is fulfilled…”

“…More precisely, we will construct a rational extension of the nonlinear oscillator potential, such that the associated solutions are expressed in terms of exceptional orthogonal polynomials [7,8]. A complete set of such polynomials, introduced in [6], has the remarkable property of forming an orthogonal system in a weighted Hilbert space, though they start with some polynomial of degree greater than or equal to one.…”

“…There exist several approaches to obtain the latter, e.g. point canonical transformation transformation [23,26,25,17], supersymmetric quantum mechanics [24,2,5,21,22], Darboux-Crum transformation [9,6], Darboux-Backlund transformation [10,11,12] and prepotential approach [13,14].…”

Bound state solution of the Schrödinger equation for Mie potential

“…Recently, NU-method has been used to solve Schrödinger equation for some well known potentials [17][18][19][20][21][22], Dirac and Klein-Gordon equations for the Coulomb and some exponential potentials. In the present work the Schrödinger equation is solved by the NU method for Mie potential with any value of angular momentum ℓ.…”