Calculation of the eigenfunctions and eigenvalues of Schr\"odinger type equations by asymptotic Taylor expansion method (ATEM)

A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues.