TY - JOUR

T1 - Solving the Kratzer oscillator in diatomic molecules

T2 - An algebraic approach based on the so(2,1) Lie algebra

AU - Maulén, Boris

AU - Gonzalez, Jose Mauricio

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd.

PY - 2021/8

Y1 - 2021/8

N2 - In this article, we solve the rovibrational Schrödinger equation for diatomic molecules using the Kratzer oscillator by means of the Lie algebra. The main contribution of our algebraic approach is that this allows us to reduce the degree of the Schrödinger equation giving thus a first-order differential equation, by which the vibrational ground state wave function is obtained, clearly and in few steps. The energies are obtained by scaling of the observables r and p r which preserves the canonical commutation relation, and a recurrence relation for the bound states written in terms of the raising operator is also given. Also we calculate the rovibrational spectrum of H 2 and CO molecules, showing that the energies of the Kratzer oscillator not only depends on vibrational and rotational quantum numbers, but also in the difference between the vibrational quantum number with its minimum value, for a fixed l. The article ends giving a physical insight of the symmetry transformation of the SO(2, 1) Lie group in order to show the relationship between this group and its associated Lie algebra. Finally, as an illustrative example, we calculated the selection rules for the vibrational quantum number, from a purely algebraic approach.

AB - In this article, we solve the rovibrational Schrödinger equation for diatomic molecules using the Kratzer oscillator by means of the Lie algebra. The main contribution of our algebraic approach is that this allows us to reduce the degree of the Schrödinger equation giving thus a first-order differential equation, by which the vibrational ground state wave function is obtained, clearly and in few steps. The energies are obtained by scaling of the observables r and p r which preserves the canonical commutation relation, and a recurrence relation for the bound states written in terms of the raising operator is also given. Also we calculate the rovibrational spectrum of H 2 and CO molecules, showing that the energies of the Kratzer oscillator not only depends on vibrational and rotational quantum numbers, but also in the difference between the vibrational quantum number with its minimum value, for a fixed l. The article ends giving a physical insight of the symmetry transformation of the SO(2, 1) Lie group in order to show the relationship between this group and its associated Lie algebra. Finally, as an illustrative example, we calculated the selection rules for the vibrational quantum number, from a purely algebraic approach.

KW - 1) Lie algebra

KW - diatomic molecules

KW - Kratzer oscillator

KW - so(2

UR - http://www.scopus.com/inward/record.url?scp=85107025759&partnerID=8YFLogxK

U2 - 10.1088/1402-4896/abfef1

DO - 10.1088/1402-4896/abfef1

M3 - Article

AN - SCOPUS:85107025759

SN - 0031-8949

VL - 96

JO - Physica Scripta

JF - Physica Scripta

IS - 8

M1 - 085401

ER -