The para--Racah Hamiltonian as an exactly solvable discretization of the P"oschl--Teller box
The para-Racah Hamiltonian is a discrete model that exactly mimics the Pöschl-Teller box when scaled up. As more sites are added, this discrete system contracts to a trigonometric Pöschl-Teller Hamiltonian on a finite interval. This connection reveals deep mathematical links between different polynomial families and quantum potentials.