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

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 potential...

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Detalles Bibliográficos
Autores principales: Fu, Meihuan, Liu, Yongwen, Shi, Jianxin, Qian, Pengbo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10684078/
https://www.ncbi.nlm.nih.gov/pubmed/38015985
http://dx.doi.org/10.1371/journal.pone.0294851
Descripción
Sumario: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.