The solution of D-dimensional Schrodinger equation for potential V(r)=ar2+br+cr-1+dr-2+er-3+fr-4 by using Ansatz method

Wea, Kristiana Nathalia; Супармі, A.; Cari, C.; Wahyulianti,

doi:10.1063/1.4995169

Cited by 2 publications

(1 citation statement)

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“…However, a better effect can be achieved if the potential function is the superposition of several power functions. The potential in the form of VðrÞ ¼ X n i¼À n a i r i is called the power function superposition potential, which has attracted attention from many researchers [1][2][3][4][5][6][7] looking for the analytical solution of the Schro ¨dinger equation with the power function superposition potential and the energy level of the quantum system. It plays an important role in promoting the development of the quantum theory and its application.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of three dimensional schrödinger equation with power function superposition potential

Fu,

Liu,

Shi

et al. 2023

PLoS ONE

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Finding an analytical solution to the Schrödinger equation with power function superposition potential is essential for the development of quantum theory. For example, the harmonic oscillator potential, Coulomb potential, and Klazer potential are all classed as power function superposition potentials. In this study, the general form of the power function superposition potential was used to decompose the second-order radial Schrödinger equation with this potential into the first-order Ricatti equation. Furthermore, two forms of the power function superposition potential are constructed with an exact analytical solution, and the exact bound-state energy level formula is obtained for these two potentials. Finally, the energy levels of some of the diatomic molecules were determined through calculation. And our results are actually consistent with those obtained by other methods.

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