462 research outputs found
Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two dimensional manifold
In this paper we prove that the two dimensional superintegrable systems with
quadratic integrals of motion on a manifold can be classified by using the
Poisson algebra of the integrals of motion. There are six general fundamental
classes of superintegrable systems. Analytic formulas for the involved
integrals are calculated in all the cases. All the known superintegrable
systems are classified as special cases of these six general classes.Comment: LaTeX, 72 pages. Extended version of the published version in JM
Dynamic and Static Excitations of a Classical Discrete Anisotropic Heisenberg Ferromagnetic Spin Chain
Using Jacobi elliptic function addition formulas and summation identities we
obtain several static and moving periodic soliton solutions of a classical
anisotropic, discrete Heisenberg spin chain with and without an external
magnetic field. We predict the dispersion relations of these nonlinear
excitations and contrast them with that of magnons and relate these findings to
the materials realized by a discrete spin chain. As limiting cases, we discuss
different forms of domain wall structures and their properties.Comment: Accepted for publication in Physica
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
On the hydrogen symmetry
We construct O(4)-invariant hydrogen wave function in coordinate representation
A q-Deformed Schr\"odinger Equation
We found hermitian realizations of the position vector , the angular
momentum and the linear momentum , all behaving like
vectors under the algebra, generated by and . They are
used to introduce a -deformed Schr\" odinger equation. Its solutions for the
particular cases of the Coulomb and the harmonic oscillator potentials are
given and briefly discussed.Comment: 14 pages, latex, no figure
Electron shielding of the nuclear magnetic moment in hydrogen-like atom
The correction to the wave function of the ground state in a hydrogen-like
atom due to an external homogenous magnetic field is found exactly in the
parameter . The projection of the correction to the wave
function of the state due to the external homogeneous magnetic field
is found for arbitrary . The projection of the correction to the
wave function of the state due to the nuclear magnetic moment is
also found for arbitrary . Using these results, we have calculated the
shielding of the nuclear magnetic moment by the electron.Comment: 15 page
Deformed oscillator algebras for two dimensional quantum superintegrable systems
Quantum superintegrable systems in two dimensions are obtained from their
classical counterparts, the quantum integrals of motion being obtained from the
corresponding classical integrals by a symmetrization procedure. For each
quantum superintegrable systema deformed oscillator algebra, characterized by a
structure function specific for each system, is constructed, the generators of
the algebra being functions of the quantum integrals of motion. The energy
eigenvalues corresponding to a state with finite dimensional degeneracy can
then be obtained in an economical way from solving a system of two equations
satisfied by the structure function, the results being in agreement to the ones
obtained from the solution of the relevant Schrodinger equation. The method
shows how quantum algebraic techniques can simplify the study of quantum
superintegrable systems, especially in two dimensions.Comment: 22 pages, THES-TP 10/93, hep-the/yymmnn
Non-linear finite -symmetries and applications in elementary systems
In this paper it is stressed that there is no {\em physical} reason for
symmetries to be linear and that Lie group theory is therefore too restrictive.
We illustrate this with some simple examples. Then we give a readable review on
the theory finite -algebras, which is an important class of non-linear
symmetries. In particular, we discuss both the classical and quantum theory and
elaborate on several aspects of their representation theory. Some new results
are presented. These include finite coadjoint orbits, real forms and
unitary representation of finite -algebras and Poincare-Birkhoff-Witt
theorems for finite -algebras. Also we present some new finite -algebras
that are not related to embeddings. At the end of the paper we
investigate how one could construct physical theories, for example gauge field
theories, that are based on non-linear algebras.Comment: 88 pages, LaTe
Comparative analysis of battery electric, hydrogen fuel cell and hybrid vehicles in a future sustainable road transport system
Accepted versio
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