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7 papers · 2 filters
The Hahn Quantum System
A D Alhaidari, Y. -T. Li
Using a formulation of quantum mechanics based on the theory of orthogonal polynomials, we introduce a four-parameter system associated with the Hahn and continuous Hahn polynomial…
Quantum mechanics with orthogonal polynomials
A. D. Alhaidari
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space wh…
Five-parameter potential box with inverse square singular boundaries
A. D. Alhaidari, T. J. Taiwo
Using the Tridiagonal Representation Approach, we obtain solutions (energy spectrum and corresponding wavefunctions) for a new five-parameter potential box with inverse square sing…
Extending the class of solvable potentials. IV Inverse square potential with a rich spectrum
A. D. Alhaidari
This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable bas…
Establishing correspondence between the reformulation of quantum mechanics without a potential function and the conventional formulation
A. D. Alhaidari
Within the recent reformulation of quantum mechanics where a potential function is not required, we show how to reconstruct the potential so that a correspondence with the standard…
Energy spectrum of a generalized Scarf potential using the Asymptotic Iteration Method and the Tridiagonal Representation Approach
S. A. Al-Buradah, H. Bahlouli, A. D. Alhaidari
The well-known trigonometric Scarf potential is generalized by adding a sinusoidal term and then treated using the Asymptotic Iteration Method (AIM) and the Tridiagonal Representat…