Using a recent formulation of quantum mechanics without potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics gives the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.We are honored to dedicate this work to Prof. Hashim A. Yamani on the occasion of his 70 th birthday.

Using the Tridiagonal Representation Approach, we obtain solutions (energy spectrum and corresponding wavefunctions) for a new five-parameter potential box with inverse square singularity at the boundaries.

No abstract

In an effort to achieve our aims (getting larger quantum systems) in the recent reformulation of quantum mechanics without potential function [1-5], we obtained a new quantum system associated with Meixner -Pollaczek orthogonal polynomial class (hereby called Meixner -Pollaczek Quantum system). The energy spectrum and wavefunction of the quantum system were given. To the best of our knowledge, this quantum system is not found in any physics literature.

In order to establish a correspondence between the reformulation of quantum mechanics without potential function and the convention quantum mechanics, we obtained the potential function of the New Wilson -Racah quantum system in [3] using any of the proposed formula in [4]. To achieve this, we used the matrix elements of the potential function and the basis element of the configuration space.