Exact Analytical Solutions of the Wave Function for Some q-Deformed Potentials

We derive analytical solutions of the Schrödinger wave equation for some q-deformed potentials. Most of these solutions are obtained in terms of Heun functions. However, for some particular cases the solutions are obtained in terms of geometric and hypergeometric functions. Different observations are realized for each potential. However, for all the cases which we study the oscillations are the usual ones. It is also noted that all of these functions are sensitive to variation in the parameters involved. Our discussion for some particular potential has shown us that for a large value of the parameter q the system tends to exhibit the energy for an infinite potential well between two points zero and a in addition to a free particle.