The relativistic quantum dynamics of the generalized Klein–Gordon (KG) oscillator having
position-dependent mass in the Gödel-type space–time is investigated. We have presented …

Taking into account the importance of the unified theory of quantum mechanics and gravity,
and the existence of a minimal length of the order of the Planck scale, we consider a …

We seek the possible polynomial solutions of the Schrödinger equation for the sextic and
decatic potentials. Under certain conditions on the parameters of the potentials, we show …

V qp (x)=− V 0 sinh p (α x)/cosh q (α x)⁠. We show that the model preserves a finite
dimensional polynomial space for some p and q. Thus using the Bethe ansatz method, we …

We study the behavior of non-relativistic quantum particles interacting with the linear
potential plus the Coulomb potential (LCP) and Kratzer potential under the generalized …

We introduce a new family of quasi-exactly solvable (QES) generalized isotonic oscillators
which are based on the Hermite exceptional orthogonal polynomials. We obtain exact …

The exact solution of the Schrödinger equation for the four quasi-exactly solvable potentials
is presented using the functional Bethe ansatz method. It is shown that all models give rise …

The symmetrized quartic polynomial oscillator is shown to admit an sl(2,R) sl (2,𝕉)
algebraization. Some simple quasi-exactly solvable (QES) solutions are exhibited. A new …

We introduce two new families of quasi-exactly solvable (QES) extensions of the oscillator in
a d-dimensional constant-curvature space. For the first three members of each family, we …

General formulae for solutions of the Schrödinger equation with power potentials are
derived. The wavefunctions are expressed as products of the asymptotic factors and special …