Twist deformation of rotationally invariant quantum mechanics

Journal Article · Mon Nov 15 04:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3506406· OSTI ID:21501198

Chakraborty, B ^[1]; Kuznetsova, Z ^[2]; Toppan, F ^[3]

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1. S.N. Bose National Center for Basic Sciences, JD Block, Sector III, Salt-Lake, Kolkata-700098 (India)
2. UFABC, Rua Catequese 242, Bairro Jardim, cep 09090-400, Santo Andre (Brazil)
3. CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)

Noncommutative quantum mechanics in 3D is investigated in the framework of an abelian Drinfeld twist which deforms a given Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential), and the Coulomb potential.

• OSTI ID: 21501198
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ANGULAR MOMENTUM
ANHARMONIC OSCILLATORS
COMMUTATION RELATIONS
COULOMB FIELD
ELECTRIC FIELDS
ENERGY
HAMILTONIANS
HARMONIC OSCILLATORS
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
POTENTIAL ENERGY
QUANTUM MECHANICS
QUANTUM OPERATORS
SYMMETRY GROUPS