A recent method called asymptotic Taylor expansion (ATEM) is appliedto determine the analytical expression for eigenfunctions and numericalresults for eigenvalues of the Schrödinger equation for the bistablepotentials. Optimal truncation of the Taylor series gives a best possibleanalytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithmconstructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistentwith the existing literature.
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