A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

Sergio A. Hojman; Felipe A. Asenjo

doi:10.1016/j.physleta.2020.126913

A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

Sergio A. Hojman, Felipe A. Asenjo

Faculty of Liberal Arts

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.

Original language	English
Article number	126913
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	384
Issue number	36
DOIs	https://doi.org/10.1016/j.physleta.2020.126913
State	Published - 30 Dec 2020

Keywords

Accelerating wavepackets
Bohm potential
New exact solutions
Schrödinger equation

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10.1016/j.physleta.2020.126913

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title = "A new approach to solve the one-dimensional Schr{\"o}dinger equation using a wavefunction potential",

abstract = "A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schr{\"o}dinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.",

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AB - A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.

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A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

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Keywords

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