Abstract
This paper presents a unified treatment of the kinetic energy matrix elements related to a number of Lagrange functions associated with the Lagrange–Jacobi mesh. The matrix elements can be readily modified for application to problems requiring eigenfunction expansion with Lagrange–Legendre, Lagrange–Chebyshev, Lagrange–Gegenbauer, as well as the Lagrange–Jacobi functions. The applicability of and the accuracy attainable with the matrix elements is demonstrated with the solution to the Schrödinger equation for confining trigonometric Pöschl–Teller potentials. The results obtained are within machine accuracy when appropriate choices of the basis functions are used.
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