TY - JOUR
T1 - On the q-deformed exponential-type potentials
AU - Ovando, G.
AU - Peña, J. J.
AU - Morales, J.
AU - García-Ravelo, J.
AU - García-Martínez, J.
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - In this work, both non-deformed and q-deformed exactly solvable multiparameter exponential-type potentials V±(r) are obtained; V+(r= x) stands for one-dimensional potential and V-(r) for the radial part of s-states used in the treatment of vibrational properties of diatomic molecules. As a first result, we show that non-deformed potentials arise from non-q-dependent parameters involved in V±(r) and rather correspond to a class of q-shifted exponential-type potentials obtained from the Arai’s q-deformed hyperbolic functions. As a second result, by using q-dependent parameters in V±(r) it is possible to obtain true q-deformed exponential-type potentials. As a useful application of these potentials, some examples of q-deformed exponential-type potentials are considered by means of a proper selection of the involved parameters. Our proposal is general and can be viewed as a unified treatment to the study of q-deformed exponential-type potentials with the advantage that it is not necessary to use a specialized method for solving the Schrödinger equation to each specific potential because many of them are obtained as particular cases of V±(r). Furthermore, new q-deformed potentials used as interesting alternatives in quantum chemical applications can be derived.
AB - In this work, both non-deformed and q-deformed exactly solvable multiparameter exponential-type potentials V±(r) are obtained; V+(r= x) stands for one-dimensional potential and V-(r) for the radial part of s-states used in the treatment of vibrational properties of diatomic molecules. As a first result, we show that non-deformed potentials arise from non-q-dependent parameters involved in V±(r) and rather correspond to a class of q-shifted exponential-type potentials obtained from the Arai’s q-deformed hyperbolic functions. As a second result, by using q-dependent parameters in V±(r) it is possible to obtain true q-deformed exponential-type potentials. As a useful application of these potentials, some examples of q-deformed exponential-type potentials are considered by means of a proper selection of the involved parameters. Our proposal is general and can be viewed as a unified treatment to the study of q-deformed exponential-type potentials with the advantage that it is not necessary to use a specialized method for solving the Schrödinger equation to each specific potential because many of them are obtained as particular cases of V±(r). Furthermore, new q-deformed potentials used as interesting alternatives in quantum chemical applications can be derived.
KW - Canonical transformation
KW - Diatomic molecules
KW - Hypergeometric DE
KW - Schrödinger-like equation
KW - q-deformed exponential-type potentials
UR - http://www.scopus.com/inward/record.url?scp=85049973119&partnerID=8YFLogxK
U2 - 10.1007/s00214-018-2289-x
DO - 10.1007/s00214-018-2289-x
M3 - Artículo
SN - 1432-881X
VL - 137
JO - Theoretical Chemistry Accounts
JF - Theoretical Chemistry Accounts
IS - 8
M1 - 111
ER -