  A recent method called Asymptotic Taylor expansion (ATEM) is applied to
determine the analytical expression for eigenfunctions and numerical results
for eigenvalues of the Schrodinger equation for the bistable potentials.
Optimal truncation of the Taylor series gives a best possible analytical
expression for eigenfunctions and numerical result for eigenvalues. It is shown
that the results are obtained by a simple algorithm constructed for a computer
system using symbolic or numerical calculation. It is observed that ATEM
produces excellent results appropriate with the existing literature.
