1,076 research outputs found
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
Optical potentials using resonance states in Supersymmetric Quantum Mechanics
Complex potentials are constructed as Darboux-deformations of short range,
radial nonsingular potentials. They behave as optical devices which both
refracts and absorbs light waves. The deformation preserves the initial
spectrum of energies and it is implemented by means of a Gamow-Siegert function
(resonance state). As straightforward example, the method is applied to the
radial square well. Analytical derivations of the involved resonances show that
they are `quantized' while the corresponding wave-functions are shown to behave
as bounded states under the broken of parity symmetry of the related
one-dimensional problem.Comment: 16 pages, 6 figures, 1 tabl
Exactly Solvable Hydrogen-like Potentials and Factorization Method
A set of factorization energies is introduced, giving rise to a
generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for
the radial hydrogen-like Hamiltonian. An algebraic intertwining technique
involving such factorization energies leads to derive -parametric families
of potentials in general almost-isospectral to the hydrogen-like radial
Hamiltonians. The construction of SUSY partner Hamiltonians with ground state
energies greater than the corresponding ground state energy of the initial
Hamiltonian is also explicitly performed.Comment: LaTex file, 21 pages, 2 PostScript figures and some references added.
To be published in J. Phys. A: Math. Gen. (1998
Bessel-Gauss beams of arbitrary integer order: propagation profile, coherence properties and quality factor
We present a novel approach to generate Bessel-Gauss modes of arbitrary
integer order and well-defined optical angular momentum in a gradient index
medium of transverse parabolic profile. The propagation and coherence
properties, as well as the quality factor, are studied using algebraic
techniques that are widely used in quantum mechanics. It is found that imposing
the well-defined optical angular momentum condition, the Lie group
comes to light as a characteristic symmetry of the Bessel-Gauss beams.Comment: 24 pages, 12 figure
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