Excited-state energy eigenvalue and wave-function evaluation of the Gaussian asymmetric double-well potential problem via numerical shooting method 2

This project aims at computation excited-state energy eigenvalues and wave-function of a particle under Gaussian asymmetric double-well 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. 2.1 and 4) The numerical shooting method is generally regarded as one of the most efficient methods that give very accurate results because it integrates the Schrodinger equation directly, though in the numerical sense. The n = even case is shown in Figs. 4, 5 and 6. In this case, the wave-function has split up on asymmetric nodes under Gaussian asymmetric double-well potential. The n = odd case is shown in Fig. 7. In this case, the wave-function has not split up on asymmetric nodes under Gaussian asymmetric double-well potential.