Lagrange distributed approximating functional method for the solution of the Schrِdinger equation

The utility and accuracy of a new distributed approximating functional (DAF), combining the Gaussian weighted DAF concept with Lagrange interpolation, is explored for the discrete spectrum solution of the Schrödinger equation. Two instructive examples, an I2 Morse oscillator and the 2-dimensional Henon–Heiles potential, are considered in the present study. The present “Lagrange DAF” (LDAF) approach achieves extremely high accuracy for I2 while using fewer grid points than previous approaches. The present results for the Henon–Heiles system are in excellent agreement with those of earlier established methods, such as that of Shizgal.