854 research outputs found
New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
New solutions for second-order intertwining relations in two-dimensional SUSY
QM are found via the repeated use of the first order supersymmetrical
transformations with intermediate constant unitary rotation. Potentials
obtained by this method - two-dimensional generalized P\"oschl-Teller
potentials - appear to be shape-invariant. The recently proposed method of
separation of variables is implemented to obtain a part of their
spectra, including the ground state. Explicit expressions for energy
eigenvalues and corresponding normalizable eigenfunctions are given in analytic
form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2;
some references adde
Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
In this paper, we continue to study factorization of supersymmetric (SUSY)
transformations in one-dimensional Quantum Mechanics into chains of elementary
Darboux transformations with nonsingular coefficients. We define the class of
potentials that are invariant under the Darboux - Crum transformations and
prove a number of lemmas and theorems substantiating the formulated formerly
conjectures on reducibility of differential operators for spectral equivalence
transformations. Analysis of the general case is performed with all the
necessary proofs.Comment: 13 page
Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra
We study possible factorizations of supersymmetric (SUSY) transformations in
the one-dimensional quantum mechanics into chains of elementary Darboux
transformations with nonsingular coefficients. A classification of irreducible
(almost) isospectral transformations and of related SUSY algebras is presented.
The detailed analysis of SUSY algebras and isospectral operators is performed
for the third-order case.Comment: 16 page
Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics
The iteration procedure of supersymmetric transformations for the
two-dimensional Schroedinger operator is implemented by means of the matrix
form of factorization in terms of matrix 2x2 supercharges. Two different types
of iterations are investigated in detail. The particular case of diagonal
initial Hamiltonian is considered, and the existence of solutions is
demonstrated. Explicit examples illustrate the construction.Comment: 15
The Standard Quantum Limit of Coherent Beam Combining
Coherent beam combining refers to the process of generating a bright output
beam by merging independent input beams with locked relative phases. We report
the first quantum mechanical noise limit calculations for coherent beam
combining and compare our results to quantum-limited amplification. Our
coherent beam combining scheme is based on an optical Fourier transformation
which renders the scheme compatible with integrated optics. The scheme can be
layed out for an arbitrary number of input beams and approaches the shot noise
limit for a large number of inputs
Asymptotic Methods in the Statics and Dynamics of Perforated Plates and Shells with Periodic Structures
 
Lorentz Symmetry Breaking in Abelian Vector-Field Models with Wess-Zumino Interaction
We consider the abelian vector-field models in the presence of the
Wess-Zumino interaction with the pseudoscalar matter. The occurence of the
dynamic breaking of Lorentz symmetry at classical and one-loop level is
described for massless and massive vector fields. This phenomenon appears to be
the non-perturbative counterpart of the perturbative renormalizability and/or
unitarity breaking in the chiral gauge theories.Comment: 11 pages,LaTeX, Preprint DFUB/94 - 1
Buckling of Cylindrical Shells of Variable Thickness, Loaded by External Uniform Pressure
From the mathematical standpoint one has a partial differential equation with variable coefficients. Perturbation procedure gives the possibilityfor an analytical solution of this eigenvalue problem. Self-adjoint equations and Padé approximants are used for improving the obtained results
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