TY - JOUR

T1 - A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

AU - Hojman, Sergio A.

AU - Asenjo, Felipe A.

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/12/30

Y1 - 2020/12/30

N2 - 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.

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.

KW - Accelerating wavepackets

KW - Bohm potential

KW - New exact solutions

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85091986114&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2020.126913

DO - 10.1016/j.physleta.2020.126913

M3 - Article

AN - SCOPUS:85091986114

VL - 384

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 36

M1 - 126913

ER -