398 research outputs found
On the new translational shape invariant potentials
Recently, several authors have found new translational shape invariant
potentials not present in classic classifications like that of Infeld and Hull.
For example, Quesne on the one hand and Bougie, Gangopadhyaya and Mallow on the
other have provided examples of them, consisting on deformations of the
classical ones. We analyze the basic properties of the new examples and observe
a compatibility equation which has to be satisfied by them. We study particular
cases of such equation and give more examples of new translational shape
invariant potentials.Comment: 9 pages, uses iopart10.clo, version
Generalized Morse Potential: Symmetry and Satellite Potentials
We study in detail the bound state spectrum of the generalized Morse
potential~(GMP), which was proposed by Deng and Fan as a potential function for
diatomic molecules. By connecting the corresponding Schr\"odinger equation with
the Laplace equation on the hyperboloid and the Schr\"odinger equation for the
P\"oschl-Teller potential, we explain the exact solvability of the problem by
an symmetry algebra, and obtain an explicit realization of the latter
as . We prove that some of the generators
connect among themselves wave functions belonging to different GMP's (called
satellite potentials). The conserved quantity is some combination of the
potential parameters instead of the level energy, as for potential algebras.
Hence, belongs to a new class of symmetry algebras. We also stress
the usefulness of our algebraic results for simplifying the calculation of
Frank-Condon factors for electromagnetic transitions between rovibrational
levels based on different electronic states.Comment: 23 pages, LaTeX, 2 figures (on request). one LaTeX problem settle
Application of nonlinear deformation algebra to a physical system with P\"oschl-Teller potential
We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31
(1998) 6473), wherein a nonlinear deformation of su(1,1) involving two
deforming functions is realized in the exactly solvable quantum-mechanical
problem with P\" oschl-Teller potential, and is used to derive the well-known
su(1,1) spectrum-generating algebra of this problem. We show that one of the
defining relations of the nonlinear algebra, presented by the authors, is only
valid in the limiting case of an infinite square well, and we determine the
correct relation in the general case. We also use it to establish the correct
link with su(1,1), as well as to provide an algebraic derivation of the
eigenfunction normalization constant.Comment: 9 pages, LaTeX, no figure
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
Multi-indexed (q-)Racah Polynomials
As the second stage of the project multi-indexed orthogonal polynomials, we
present, in the framework of `discrete quantum mechanics' with real shifts in
one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from
the (q-)Racah polynomials by multiple application of the discrete analogue of
the Darboux transformations or the Crum-Krein-Adler deletion of `virtual state'
vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials
reported earlier. The virtual state vectors are the `solutions' of the matrix
Schr\"odinger equation with negative `eigenvalues', except for one of the two
boundary points.Comment: 29 pages. The type II (q-)Racah polynomials are deleted because they
can be obtained from the type I polynomials. To appear in J.Phys.
Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
Known shape-invariant potentials for the constant-mass Schrodinger equation
are taken as effective potentials in a position-dependent effective mass (PDEM)
one. The corresponding shape-invariance condition turns out to be deformed. Its
solvability imposes the form of both the deformed superpotential and the PDEM.
A lot of new exactly solvable potentials associated with a PDEM background are
generated in this way. A novel and important condition restricting the
existence of bound states whenever the PDEM vanishes at an end point of the
interval is identified. In some cases, the bound-state spectrum results from a
smooth deformation of that of the conventional shape-invariant potential used
in the construction. In others, one observes a generation or suppression of
bound states, depending on the mass-parameter values. The corresponding
wavefunctions are given in terms of some deformed classical orthogonal
polynomials.Comment: 26 pages, no figure, reduced secs. 4 and 5, final version to appear
in JP
N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane
The family of Tremblay-Turbiner-Winternitz Hamiltonians on a plane,
corresponding to any positive real value of , is shown to admit a supersymmetric extension of the same kind as that introduced by Freedman
and Mende for the Calogero problem and based on an superalgebra. The irreducible representations of the latter
are characterized by the quantum number specifying the eigenvalues of the first
integral of motion of . Bases for them are explicitly constructed.
The ground state of each supersymmetrized Hamiltonian is shown to belong to an
atypical lowest-weight state irreducible representation.Comment: 18 pages, no figur
Real time omplementations of the Nagao image smoothing filter
We present varions ASIC implementations of the Nagao smoothing filter . This
filter is used to segment non textural pictures with an edge détection approach .
Some changes of the initial algorithm are tested both in term of complexity
and performance. Hardware implementations are compared for speed and for
silicon area used. Design aspects, like pipelining and maxima computation are
discussed.Dans ce papier, nous présentons différentes implantations ASIC d'une version modifiée du filtre de lissage de Nagao utilisé dans une chaîne de segmentation par les contours d'images non texturées pour le contrôle de fabrication. Différentes variantes de l'algorithme initial de Nagao sont comparées en performance et complexité de réalisation. Différentes solutions architecturales matérielles d'une de ces variantes appelée Nagmod sont critiquées en terme de surface et rapidité. Certains aspects du design: l'exploitation du pipeline, la structure d'un opérateur de recherche de maximum sont discuté
Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics
In recent years, one of the most interesting developments in quantum
mechanics has been the construction of new exactly solvable potentials
connected with the appearance of families of exceptional orthogonal polynomials
(EOP) in mathematical physics. In contrast with families of (Jacobi, Laguerre
and Hermite) classical orthogonal polynomials, which start with a constant, the
EOP families begin with some polynomial of degree greater than or equal to one,
but still form complete, orthogonal sets with respect to some positive-definite
measure. We show how they may appear in the bound-state wavefunctions of some
rational extensions of well-known exactly solvable quantum potentials. Such
rational extensions are most easily constructed in the framework of
supersymmetric quantum mechanics (SUSYQM), where they give rise to a new class
of translationally shape invariant potentials. We review the most recent
results in this field, which use higher-order SUSYQM. We also comment on some
recent re-examinations of the shape invariance condition, which are independent
of the EOP construction problem.Comment: 21 pages, no figure; communication at the Symposium Symmetries in
Science XV, July 31-August 5, 2011, Bregenz, Austri
Generalized boson algebra and its entangled bipartite coherent states
Starting with a given generalized boson algebra U_(h(1)) known as the
bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ
the Hopf duality arguments to provide the dually conjugate function algebra
Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a
closed form expression of the universal T matrix that caps the duality and
generalizes the familiar exponential map relating a Lie algebra with its
corresponding group. Subsequently, using an inverse Mellin transform approach,
the coherent states of single-node systems subject to the U_(h(1)) symmetry
are found to be complete with a positive-definite integration measure.
Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to
generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur
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