Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics E

Two Parameter Quantum Deformation of U(2) ⊃ U(1) Dynamical Symmetry and the Vibrational Spectra of Diatomic Molecules

Ramandeep S. Johal, Raj K. Gupta

Published Oct 1, 1998• 20 citations
Publisher

Abstract

The vibrational spectra in H2-molecule is studied by taking the two parameter quantum deformed Uqp(u2) ⊃ Uqp(u1) algebra as the model for the system. The results are improved, compared with the classical as well as the one parameter q-description. The fitting parameter remains the same (at most two) in both cases of q– and qp–deformations.

DOI
10.1142/s0218301398000294

Related papers

U q (4)⊇O q(4) description of diatomic molecules: Vibrational spectra

Raj K. Gupta, Ian L. Cooper

Quantum-deformed algebra (q-DA) of the O(4) dynamical symmetry of the U(4) group is studied in respect of the vibrational spectra of diatomic molecules. It is shown that, as in the case of the U(6) group for nuclei, the q-deformation parameter in Uq(4)⊇Oq(4) must also be complex for any meaningful gain in going from the classical to the q-deformed algebra. Application is made to the ground electronic state (X 1Σ+g) of the H2 molecule.

The Journal of Chemical Physics•Feb 22, 1995•7 citations

A qp-DEFORMED ANHARMONIC OSCILLATOR WITH THE Uqp(U2) ⊃ Uqp( O 2) SYMMETRY AND ITS APPLICATION TO VIBRATIONAL MOLECULAR SPECTRA

Huan-Qiang Zhou, Xinming Zhang, Jingsong He

A qp-deformed anharmonic oscillator with the Uqp(U2) ⊃ Uqp(O2) symmetry is presented for describing vibrational spectra of diatomic molecules. The energy formula is tested on the vibrational spectra in the state [Formula: see text] of H2 obtained through the Rydberg-Klein-Rees (RKR) method.

Modern Physics Letters B•Jul 20, 1995•2 citations

Uq(2)⊃Uq(1) DESCRIPTION OF VIBRATIONAL SPECTRA OF DIATOMIC MOLECULES

RAJ K. GUPTA, Ramandeep S. Johal, Ian L. Cooper

q-deformation of the U(1) dynamical symmetry of U(2) group is introduced for the first time for vibrations of diatomic molecules. The question of pure real and pure imaginary value of q-deformation parameter, often raised in the literature, is found to be related to the particular choice of the constants of the model. The complex q-deformation parameter is allowed, with pure real and pure imaginary values as its special cases. Compared to the other dynamical symmetry Oq(2) of Uq(2), the result of Uq(1) of Uq(2) remains better even when the vibron number in Oq(2) is varied. The role of the vibron number in the two dynamical symmetries of U(2) is shown to be different. In Uq(1) symmetry, the vibron number is fixed by the number of observed states of the system since Uq(1) represents the q-deformation of a truncated anharmonic oscillator. A possible physical meaning to the q-deformation parameter is suggested in terms of higher order anharmonicities of the truncated anharmonic oscillator.

Modern Physics Letters A•Nov 10, 1996•4 citations

Diatomic-molecular spectrum in view of quantum group theory

Zhe Chang, Hong Yan

We suggest the quantum Heisenberg group ${\mathit{H}}_{\mathit{q}(\mathit{J})}$(4) as the dynamical symmetry group of a diatomic-molecule system. The deformation parameter q of the ${\mathit{H}}_{\mathit{q}(\mathit{J})}$(4) symmetry group is a function of J (the quantum number of the angular momentum of the rigid rotation) and characterizes the interaction between vibration and rotation. The vibrational and rotational structures of diatomic molecules are compactly expressed using the quantum-group-theoretic approach. Taylor expansions of the analytic formulas from this approach reproduce the results of the anharmonic-oscillator and the nonrigid-rotator models. For some randomly selected molecules in particular states, the parameters are computed to fit the phenomenological formulas to high accuracy.

Physical Review A•Dec 1, 1991•21 citations

q-deformed vibron model for diatomic molecules

R. N. Alvarez, Dennis Bonatsos A, Yu.F. Smirnov

A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries of the model are rewritten, using the concept of complementary subalgebras, in a more convenient form, which is subsequently deformed. The present model unifies the so far independent successful quantum-algebraic approaches to rotational and to vibrational spectra of diatomic molecules. In addition, the method can be used for the construction of deformed versions of the U(5) and O(6) limits of the interacting boson model of nuclear structure.

Physical Review A•Aug 1, 1994•25 citations

A System of Interest in Spectroscopy: The qp-Rotor System

R. Barbier, M. Kibler

A rotor system, having the symmetry afforded by the two-parameter quantum algebra Uqp(u(2)), is investigated in this communication. This system is useful in rotational spectroscopy of molecules and nuclei. In particular, it is shown to lead to a model (viz., the qp-rotor model) for describing (via an energy formula and a qp-deformation of E2 reduced transition probabilities) rotational bands of deformed and superdeformed nuclei.

arXiv:nucl-th/9911061•Nov 17, 1999•0 citations
The vibrational spectra in H2-molecule is studied by taking the two parameter quantum deformed Uqp(u2) ⊃ Uqp(u1) algebra as the model for the system. The results are improved, compared with the classical as well as the one parameter q-description. The fitting parameter remains the same (at most two) in both cases of q– and qp–deformations.
q-deformation of the U(1) dynamical symmetry of U(2) group is introduced for the first time for vibrations of diatomic molecules. The question of pure real and pure imaginary value of q-deformation parameter, often raised in the literature, is found to be related to the particular choice of the constants of the model. The complex q-deformation parameter is allowed, with pure real and pure imaginary values as its special cases. Compared to the other dynamical symmetry Oq(2) of Uq(2), the result of Uq(1) of Uq(2) remains better even when the vibron number in Oq(2) is varied. The role of the vibron number in the two dynamical symmetries of U(2) is shown to be different. In Uq(1) symmetry, the vibron number is fixed by the number of observed states of the system since Uq(1) represents the q-deformation of a truncated anharmonic oscillator. A possible physical meaning to the q-deformation parameter is suggested in terms of higher order anharmonicities of the truncated anharmonic oscillator.
We suggest the quantum Heisenberg group Hq(J){\mathit{H}}_{\mathit{q}(\mathit{J})}Hq(J)​(4) as the dynamical symmetry group of a diatomic-molecule system. The deformation parameter q of the Hq(J){\mathit{H}}_{\mathit{q}(\mathit{J})}Hq(J)​(4) symmetry group is a function of J (the quantum number of the angular momentum of the rigid rotation) and characterizes the interaction between vibration and rotation. The vibrational and rotational structures of diatomic molecules are compactly expressed using the quantum-group-theoretic approach. Taylor expansions of the analytic formulas from this approach reproduce the results of the anharmonic-oscillator and the nonrigid-rotator models. For some randomly selected molecules in particular states, the parameters are computed to fit the phenomenological formulas to high accuracy.
A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries of the model are rewritten, using the concept of complementary subalgebras, in a more convenient form, which is subsequently deformed. The present model unifies the so far independent successful quantum-algebraic approaches to rotational and to vibrational spectra of diatomic molecules. In addition, the method can be used for the construction of deformed versions of the U(5) and O(6) limits of the interacting boson model of nuclear structure.