WKB approximation in deformed space with minimal length

The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate quantum numbers and can be invalid for small as well as very large quantum numbers. The correctness of the rule is verified by comparing obtained results with exact expressions for corresponding spectra.Comment: 13 pages Now it is avaible at http://stacks.iop.org/0305-4470/39/37

Potential algebra approach to position dependent mass Schroedinger equation

It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant potentials

One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde

Coloured extension of GL_q(2) and its dual algebra

We address the problem of duality between the coloured extension of the quantised algebra of functions on a group and that of its quantised universal enveloping algebra i.e. its dual. In particular, we derive explicitly the algebra dual to the coloured extension of GL_q(2) using the coloured RLL relations and exhibit its Hopf structure. This leads to a coloured generalisation of the R-matrix procedure to construct a bicovariant differential calculus on the coloured version of GL_q(2). In addition, we also propose a coloured generalisation of the geometric approach to quantum group duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceeding

Vector Coherent State Realization of Representations of the Affine Lie Algebra sl^(2)\hat{sl}(2)

The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as special cases.Comment: 8 pages plain latex. To appear in J. Phys.

q-Analogue of Am−1⊕An−1⊂Amn−1A_{m-1}\oplus A_{n-1}\subset A_{mn-1}

A natural embedding $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\mathcal{A}_q^{-}$ (mn)$\sim {\otimes} ^n \mathcal{A}_q^{-}$(m)$\sim {\otimes}^m\mathcal{A}_q^{-}$(n) algebras.Comment: 11 pages, no figures. In memory of professor R. P. Rousse

Effect of Minimal lengths on Electron Magnetism

We study the magnetic properties of electron in a constant magnetic field and confined by a isotropic two dimensional harmonic oscillator on a space where the coordinates and momenta operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions. We prove that the usual degeneracy of Landau levels is removed by the presence of the minimal length in the limits of weak and strong magnetic field.The thermodynamical properties of the system, at high temperature, are also investigated showing a new magnetic behavior in terms of the minimal length.Comment: 14 pages, 1 figur

The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model

The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a relativistic theory our previous findings on nonrelativistic oscillator where they were known under the name of `spin-orbit pendulum'. There are important relativistic effects (lack of periodicity, zitterbewegung, negative energy states). Many of them disappear after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate postscript figure

Non-Hermitian von Roos Hamiltonian's η\eta-weak-pseudo-Hermiticity, isospectrality and exact solvability

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables, the $\eta$-weak-pseudo-Hermitian von Roos Hamiltonians H(x) are mapped into the traditional Schrodinger Hamiltonian form H(q), where exact isospectral correspondence between H(x) and H(q) is obtained. Under a user-friendly position dependent mass settings, it is observed that for each exactly-solvable $\eta$-weak-pseudo-Hermitian reference-Hamiltonian H(q)there is a set of exactly-solvable $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians H(x). A non-Hermitian PT-symmetric Scarf II and a non-Hermitian periodic-type PT-symmetric Samsonov-Roy potentials are used as reference models and the corresponding $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.Comment: 11 pages, no figures

Ordering ambiguity revisited via position dependent mass pseudo-momentum operators

Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. An affine locally scaled first order differential introduced, in Eq.(9), as a PDM-pseudo-momentum operator. Upon intertwining our Hamiltonian, which is the sum of the square of this operator and the potential function, with the von Roos d-dimensional PDM-Hamiltonian, we observed that the so-called von Roos ambiguity parameters are strictly determined, but not necessarily unique. Our new ambiguity parameters' setting is subjected to Dutra's and Almeida's [11] reliability test and classified as good ordering.Comment: 10 pages, no figures, revised/expanded, mathematical presentations in section 2 (Especially, the typological Errors in Eqs.(9)-(12))are now corrected. To appear in the Int. J. Theor. Phy