5,636 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
Quantum mechanical spectral engineering by scaling intertwining
Using the concept of spectral engineering we explore the possibilities of
building potentials with prescribed spectra offered by a modified intertwining
technique involving operators which are the product of a standard first-order
intertwiner and a unitary scaling. In the same context we study the iterations
of such transformations finding that the scaling intertwining provides a
different and richer mechanism in designing quantum spectra with respect to
that given by the standard intertwiningComment: 8 twocolumn pages, 5 figure
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
Wronskian formula for confluent second-order supersymmetric quantum mechanics
The confluent second-order supersymmetric quantum mechanics, for which the
factorization energies tend to a single value, is studied. We show that the
Wronskian formula remains valid if generalized eigenfunctions are taken as seed
solutions. The confluent algorithm is used to generate SUSY partners of the
Coulomb potential.Comment: 7 pages, 1 figure, to be published in Physics Letters
Upper and lower nearly (i, j)-continuous multifunctions
In this paper the authors introduce and study upper and lower nearly
(I,J)-continuous multifunctions. Some characterizations and several properties concerning upper (lower) nearly (I,J)-continuous multifunctions are obtained. The results
improves many results in Literature
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
On the hereditary character of new strong variations of weyl type theorems
Berkani and Kachad [18], [19], and Sanabria et al. [32], introduced and studied
strong variations of Weyl type Theorems. In this paper, we study the behavior of these
strong variations of Weyl type theorems for an operator T on a proper closed and Tinvariant subspace W ⊆ X such that T
n
(X) ⊆ W for some n ≥ 1, where T ∈ L(X) and
X is an infinite-dimensional complex Banach space. The main purpose of this paper is to
prove that for these subspaces (which generalize the case T
n
(X) closed for some n ≥ 0),
these strong variations of Weyl type theorems are preserved from T to its restriction on W
and vice-versa. As consequence of our results, we give sufficient conditions for which these
strong variations of Weyl type Theorems are equivalent for two given operators. Also, some
applications to multiplication operators acting on the boundary variation space BV [0, 1]
are given
Weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions
The purpose of the present paper is to introduce, study
and characterize upper and lower weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions.
Also, we investigate its relation with another class of continuous multifunctions.
AMS Subject Classification: 54C10, 54C08, 54C05,
54C6
A note on preservation of generalized fredholm spectra in berkani’s sense
In this paper, we study the relationships between the spectra derived from B-Fredholm theory
corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient
conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators
are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an
operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral
properties corresponding to two given operators are the same. As application of our results, we obtain
conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm
theory are the same
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