Abstract
This work aims at computing excited-state energy eigenvalues and wave-function of a particle under Gaussian symmetric double-wells potential using numerical shooting method and perturbation theory a method to deal with discrete-eigenvalue problems. We also compare the energy eigenvalue and wave-function with those obtained from other typical means popular among physics students, namely the numerical shooting method and perturbation theory. Show that the idea of program of the numerical shooting method and perturbation theory of this problem (see Sects. 2.2 and 3). The numerical shooting method is generally regarded as one of the most efficient methods that give very accurate results because it integrates the Schrödinger equation directly, though in the numerical sense. The n = even case is shown in Fig. 5. In this case, the wave-function has split up on symmetric nodes under Gaussian symmetric double-well potential.
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Boonchui, S., Hutem, A. Excited-state energy eigenvalue and wave-function evaluation of the Gaussian symmetric double-well potential problem via numerical shooting method 1. J Math Chem 50, 1582–1597 (2012). https://doi.org/10.1007/s10910-012-9996-7
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DOI: https://doi.org/10.1007/s10910-012-9996-7