This is the unspecified version of the paper.This version of the publication may differ from the final published version. We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg's uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest's theorem hold at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented. Permanent repository link

By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U (h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U F (h) are shown to be induced from a more "fundamental" Hopf algebra obtained from the Schrödinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of the super-algebra osp(1|2n). We also discuss the possible implications in the context of quantum statistics.

Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh.The quantization scheme makes use of the so-called "unfolded formalism" discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators).The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles.

Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the single-particle Hamiltonians is computed. The multi-particle Hamiltonians are fixed, unambiguously, by the Hopf algebra coproduct. The symmetry under particle exchange is guaranteed. In d = 2 dimensions the rotational invariance is preserved, while in d = 3 the so(3) rotational invariance is broken down to an so(2) invariance.

In this work we investigate the q-deformation of the so(4) dynamical symmetry of the hydrogen atom using the theory of the quantum group su q (2). We derive the energy spectrum in a physically consistent manner and find a degeneracy breaking as well as a smaller Hilbert space. We point out that using the deformed Casimir as was done before leads to inconsistencies in the physical interpretation of the theory.