Relativistic quantum mechanics and a few applications in nuclear physics and in carbon nanotubes

• Grant number: 06/03347-8
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2006
• End date: October 31, 2008
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Antonio Soares de Castro
• Grantee: Antonio Soares de Castro
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

In 3+1 dimensions, the relations between the isospectrality for spin-0 and spin-1/2 particles and pseudospin and pseudospin symmetries in the presence of scalar and vector potentials will be investigated. With applications in nuclear physics, the existence of antiparticles states in the presence of a mixed scalar-vector-tensor Woods-Saxon potential will also ivestigated. Assuming confinement on a cylindrical surface, the solutions of the Klein-Gordon and the Dirac equations will be investigated in a nanoscale, using several sorts of potentials acting on the cylindrical surface. In 1+1 dimensions, the existence of equivalent pairs of scalar potentials will be investigated in the Klein-Gordon equation as well as in the Dirac equation. The scattering, the bound states and the confinement will be investigated for a variety of couplings and functional forms for the potentials. Time-dependent potentials will also be investigated. (AU)