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 $dV/dr$. If $dV/dr = 0$, 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 $dV/dr \sim 0$. 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