52 research outputs found
Symmetry algebra of a generalized anisotropic harmonic oscillator
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra
A square root of the harmonic oscillator
Allowing for the inclusion of the parity operator, it is possible to
construct an oscillator model whose Hamiltonian admits an EXACT square root,
which is different from the conventional approach based on creation and
annihilation operators. We outline such a model, the method of solution and
some generalizations.Comment: RevTex, 10 pages in preprint form, no figure
Noether's Theorem and time-dependent quantum invariants
The time dependent-integrals of motion, linear in position and momentum
operators, of a quantum system are extracted from Noether's theorem
prescription by means of special time-dependent variations of coordinates. For
the stationary case of the generalized two-dimensional harmonic oscillator, the
time-independent integrals of motion are shown to correspond to special
Bragg-type symmetry properties. A detailed study for the non-stationary case of
this quantum system is presented. The linear integrals of motion are
constructed explicitly for the case of varying mass and coupling strength. They
are obtained also from Noether's theorem. The general treatment for a
multi-dimensional quadratic system is indicated, and it is shown that the
time-dependent variations that give rise to the linear invariants, as conserved
quantities, satisfy the corresponding classical homogeneous equations of motion
for the coordinates.Comment: Plain TeX, 23 pages, preprint of Instituto de Ciencias Nucleares,
UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 01 (1994
Bell's inequalities in the tomographic representation
The tomographic approach to quantum mechanics is revisited as a direct tool
to investigate violation of Bell-like inequalities. Since quantum tomograms are
well defined probability distributions, the tomographic approach is emphasized
to be the most natural one to compare the predictions of classical and quantum
theory. Examples of inequalities for two qubits an two qutrits are considered
in the tomographic probability representation of spin states.Comment: 11 pages, comments and references adde
Relativistic Mean Field Approach and the Pseudo-Spin Symmetry
Based on the Relativistic Mean Field (RMF) approach the existence of the
broken pseudo-spin symmetry is investigated. Both spherical RMF and constrained
deformed RMF calculations are carried out employing realistic Lagrangian
parameters for spherical and for deformed sample nuclei. The quasi - degenerate
pseudo-spin doublets are confirmed to exist near the fermi surface for both
spherical and deformed nuclei.Comment: 9 pages RevTex, 4 p.s figures, to appear in Phys. Rev. C as R.
The pseudo-spin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line
Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the
pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn
isotopes from the proton drip line to the neutron drip line. The quality of the
pseudo-spin approximation is shown to be connected with the competition between
the centrifugal barrier (CB) and the pseudo-spin orbital potential (PSOP). The
PSOP depends on the derivative of the difference between the scalar and vector
potentials . If , the pseudo-spin symmetry is exact. The
pseudo-spin symmetry is found to be a good approximation for normal nuclei and
to become much better for exotic nuclei with highly diffuse potential, which
have . The energy splitting of the pseudo-spin partners is
smaller for orbitals near the Fermi surface (even in the continuum) than the
deeply bound orbitals. The lower components of the Dirac wave functions for the
pseudo-spin partners are very similar and almost equal in magnitude.Comment: 22 pages, 9figure
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