2,852 research outputs found
Refined Factorizations of Solvable Potentials
A generalization of the factorization technique is shown to be a powerful
algebraic tool to discover further properties of a class of integrable systems
in Quantum Mechanics. The method is applied in the study of radial oscillator,
Morse and Coulomb potentials to obtain a wide set of raising and lowering
operators, and to show clearly the connection that link these systems.Comment: 11 pages, LaTeX file, no figure
The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
We prove that the extended Poincare group in (1+1) dimensions is
non-nilpotent solvable exponential, and therefore that it belongs to type I. We
determine its first and second cohomology groups in order to work out a
classification of the two-dimensional relativistic elementary systems.
Moreover, all irreducible unitary representations of the extended Poincare
group are constructed by the orbit method. The most physically interesting
class of irreducible representations corresponds to the anomaly-free
relativistic particle in (1+1) dimensions, which cannot be fully quantized.
However, we show that the corresponding coadjoint orbit of the extended
Poincare group determines a covariant maximal polynomial quantization by
unbounded operators, which is enough to ensure that the associated quantum
dynamical problem can be consistently solved, thus providing a physical
interpretation for this particular class of representations.Comment: 12 pages, Revtex 4, letter paper; Revised version of paper published
in J. Math. Phys. 45, 1156 (2004
Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R.
Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the
non-standard (Jordanian) quantum sl(2,R) algebra is used to construct the twist
maps for two different non-standard quantum deformations of the (1+1)
Schrodinger algebra. Such deformations are, respectively, the symmetry algebras
of a space and a time uniform lattice discretization of the (1+1) free
Schrodinger equation. It is shown that the corresponding twist maps connect the
usual Lie symmetry approach to these discrete equations with non-standard
quantum deformations. This relationship leads to a clear interpretation of the
deformation parameter as the step of the uniform (space or time) lattice.Comment: 16 pages, LaTe
Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is
revisited in the context of canonical raising and lowering operators. The
Hamiltonian is then factorized in terms of two not mutually adjoint factorizing
operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The
set of eigenvalues of this new Hamiltonian is exactly the same as the energy
spectrum of the radial oscillator and the new square-integrable eigenfunctions
are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure
The supersymmetric modified Poschl-Teller and delta-well potentials
New supersymmetric partners of the modified Poschl-Teller and the Dirac's
delta well potentials are constructed in closed form. The resulting
one-parametric potentials are shown to be interrelated by a limiting process.
The range of values of the parameters for which these potentials are free of
singularities is exactly determined. The construction of higher order
supersymmetric partner potentials is also investigated.Comment: 20 pages, LaTeX file, 4 eps figure
Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
It is shown that the radial part of the Hydrogen Hamiltonian factorizes as
the product of two not mutually adjoint first order differential operators plus
a complex constant epsilon. The 1-susy approach is used to construct
non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian
Hamiltonians are shown to admit an extra `complex energy' at epsilon. New
self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy
transformation with complex conjugate pairs epsilon, (c.c) epsilon.Comment: LaTeX2e file, 13 pages, 6 EPS figures. New references added. The
present is a reorganized and simplified versio
New time-type and space-type non-standard quantum algebras and discrete symmetries
Starting from the classical r-matrix of the non-standard (or Jordanian)
quantum deformation of the sl(2,R) algebra, new triangular quantum deformations
for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously
constructed by using a graded contraction scheme; these are realized as
deformations of conformal algebras of (1+1)-dimensional spacetimes. Time-type
and space-type quantum algebras are considered according to the generator that
remains primitive after deformation: either the time or the space translation,
respectively. Furthermore by introducing differential-difference conformal
realizations, these families of quantum algebras are shown to be the symmetry
algebras of either a time or a space discretization of (1+1)-dimensional (wave
and Laplace) equations on uniform lattices; the relationship with the known Lie
symmetry approach to these discrete equations is established by means of twist
maps.Comment: 17 pages, LaTe
The role of HO_x in super- and subsonic aircraft exhaust plumes
The generation of sulfuric acid aerosols in aircraft exhaust has emerged as a critical issue in determining the impact of supersonic aircraft on stratospheric ozone. It has long been held that the first step in the mechanism of aerosol formation is the oxidation of SO_(2) emitted from the engine by OH in the exhaust plume. We report in situ measurements of OH and HO_(2) in the exhaust plumes of a supersonic (Air France Concorde) and a subsonic (NASA ER-2) aircraft in the lower stratosphere. These measurements imply that reactions with OH are responsible for oxidizing only a small fraction of SO_(2) (2%), and thus cannot explain the large number of particles observed in the exhaust wake of the Concorde
The role of HO\u3csub\u3ex\u3c/sub\u3e in super- And subsonic aircraft exhaust plumes
The generation of sulfuric acid aerosols in aircraft exhaust has emerged as a critical issue in determining the impact of supersonic aircraft on stratospheric ozone. It has long been held that the first step in the mechanism of aerosol formation is the oxidation of SO2 emitted from the engine by OH in the exhaust plume. We report in situ measurements of OH and HO2 in the exhaust plumes of a supersonic (Air France Concorde) and a subsonic (NASA ER-2) aircraft in the lower stratosphere. These measurements imply that reactions with OH are responsible for oxidizing only a small fraction of SO2 (2%), and thus cannot explain the large number of particles observed in the exhaust wake of the Concorde
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