TY - JOUR
T1 - Non-deformed singular and non-singular exponential-type potentials
AU - Pe na, J. J.
AU - Ovando, G.
AU - Morales, J.
AU - García-Ravelo, J.
N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - The canonical transformation method applied to the Schrödinger equation to transform it into a second-order differential equation of hypergeometric-type is presented. Starting from there, those exactly solvable multiparameter exponential-type (ME-T) potentials with hypergeometric wavefunctions that belong to the families of radial (singular) and one-dimensional (non-singular) potentials, are obtained. Furthermore, we show how the choice of the involved parameters leads, as particular cases, to different deformed or non-deformed potential models already used in the study of electronic properties of diatomic molecules. Also, the analysis of parameters lets us identify the couple of potential partners (singular/non-singular) that correspond to each choice of the parameters appearing in the ME-T potential. As a useful application of the proposal, the most important non-deformed exponential potential models are considered for which it can be viewed as a unified treatment with the following advantages: (1) It is not necessary to use a special method to solve the Schrödinger equation for a specific potential model because solution is obtained as particular case by the simple choice of the involved parameters; (2) The families of singular and non-singular potentials are straightforward identified; (3) The corresponding associated partners, between radial and one-dimensional non-deformed potentials, are found; (4) New potentials, as interesting alternatives for quantum applications, are obtained. In addition, from the conditions that parameters must meet to have physically acceptable solutions, we establish the requirements for the existence or not of singular/non-singular potential partners.
AB - The canonical transformation method applied to the Schrödinger equation to transform it into a second-order differential equation of hypergeometric-type is presented. Starting from there, those exactly solvable multiparameter exponential-type (ME-T) potentials with hypergeometric wavefunctions that belong to the families of radial (singular) and one-dimensional (non-singular) potentials, are obtained. Furthermore, we show how the choice of the involved parameters leads, as particular cases, to different deformed or non-deformed potential models already used in the study of electronic properties of diatomic molecules. Also, the analysis of parameters lets us identify the couple of potential partners (singular/non-singular) that correspond to each choice of the parameters appearing in the ME-T potential. As a useful application of the proposal, the most important non-deformed exponential potential models are considered for which it can be viewed as a unified treatment with the following advantages: (1) It is not necessary to use a special method to solve the Schrödinger equation for a specific potential model because solution is obtained as particular case by the simple choice of the involved parameters; (2) The families of singular and non-singular potentials are straightforward identified; (3) The corresponding associated partners, between radial and one-dimensional non-deformed potentials, are found; (4) New potentials, as interesting alternatives for quantum applications, are obtained. In addition, from the conditions that parameters must meet to have physically acceptable solutions, we establish the requirements for the existence or not of singular/non-singular potential partners.
KW - Canonical transformation
KW - Exponential-type potentials
KW - Schrödinger and hypergeometric DE
UR - http://www.scopus.com/inward/record.url?scp=85027873380&partnerID=8YFLogxK
U2 - 10.1007/s00894-017-3423-8
DO - 10.1007/s00894-017-3423-8
M3 - Artículo
C2 - 28821972
SN - 1610-2940
VL - 23
JO - Journal of Molecular Modeling
JF - Journal of Molecular Modeling
IS - 9
M1 - 265
ER -