A Method of Constructing Superpotentials by Combining Two Functions Based on Shape Invariance

Wenxin Qiu, Yin Yin, Wei Cheng, Yao Liu, Guang Luo and Antonio Scarfone

Advances in Mathematical Physics, 2024, vol. 2024, 1-12

Abstract: Supersymmetric quantum mechanics (SUSYQM) plays an important role in solving the Schrödinger equation, and it is also important to find more superpotentials that can be solved accurately. On the basis of studying the characteristics of existing superpotentials, the authors find a missing superpotential and put forward a method by combining two functions to construct all existing solvable superpotentials and prove the existence of the missing superpotential. First, based on the idea of SUSYQM, this paper studies the shape invariance of the partner potentials with the form of two functions and obtains the energy spectrum in many different cases. Second, according to the results of solving differential equations satisfied by two functions, the authors not only construct most existing solvable superpotentials successfully but also generate a missing solvable superpotential. Third, for the missing solvable superpotential, some discussions are made, such as the corresponding partner potentials, energy spectrum, ground state wave function, and excited state wave functions. Lastly, the summary is made, and the prospects are projected.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:2327044

DOI: 10.1155/2024/2327044

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