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
SN - 0375-9601
VL - 384
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 36
M1 - 126913
ER -