Free particle in \(q\)-deformed configuration space

DOI10.1007/BF00420233zbMath0813.46017MaRDI QIDQ1803235

Wolfgang Weich, Arthur Hebecker

Publication date: 29 June 1993

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

total angular momentumspectrum of the Hamiltonian\(\text{SO}_ q(N)\)-invariant Schrödinger equation for the free particleHilbert space of radial functionspartial differential equation in noncommutative geometry

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative differential geometry (46L87) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Applications of functional analysis in quantum physics (46N50) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items

The limit transition q→1 of the q-Fourier transform ⋮ Integration on quantum Euclidean space and sphere ⋮ Realization of \(U_ q(so(N))\) within the differential algebra on \(\mathbb{R}_ q^ N\) ⋮ Algebraic q-integration and Fourier theory on quantum and braided spaces ⋮ On the deformability of Heisenberg algebras ⋮ New deformed boson algebra ⋮ ON THE HERMITICITY OF q-DIFFERENTIAL OPERATORS AND FORMS ON THE QUANTUM EUCLIDEAN SPACES $\mathbb{R}_q^N$ ⋮ Field theory on the \(q\)-deformed fuzzy sphere. II: Quantization

Cites Work

• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Bicovariant differential calculus on quantum groups \(SU_ q(N)\) and \(SO_ q(N)\)
• Reality in the differential calculus on \(q\)-Euclidean spaces
• Differential calculus on compact matrix pseudogroups (quantum groups)

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