Application of the asymptotic Taylor expansion method to bistable potentials. (English) Zbl 1292.81056
Summary: A recent method called Asymptotic Taylor Expansion Method (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results 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 consistent with the existing literature.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
Keywords:
asymptotic Taylor expansion method; bistable potentials; analytical expression for eigenfunctions; numerical results for eigenvaluesSoftware:
MathematicaReferences:
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