Regularization in the J-matrix method of scattering revisited

We present an alternative, but equivalent, approach to the regularization of the reference problem in the J-matrix method of scattering. After identifying the regular solution of the reference wave equation with the “sine-like” solution in the J-matrix approach we proceed by direct integration   to find the expansion coefficients in an L²$L^2$ basis set that ensures a tridiagonal representation of the reference Hamiltonian. A differential equation in the energy is then deduced for these coefficients. The second independent solution of this equation, called the “cosine-like” solution, is derived by requiring it to pertain to the L²$L^2$ space. These requirements lead to solutions that are exactly identical to those obtained in the classical J-matrix approach. We find the present approach to be more direct and transparent than the classical differential approach of the J-matrix method.     

A phase I, randomized study of combined IL-2 and therapeutic immunisation with antiretroviral therapy

Background  

Fully functional HIV-1-specific CD8 and CD4 effector T-cell responses are vital to the containment of viral activity and disease progression. These responses are lacking in HIV-1-infected patients with progressive disease. We attempted to augment fully functional HIV-1-specific CD8 and CD4 effector T-cell responses in patients with advanced chronic HIV-1 infection.     

Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials

A systematic and intuitive approach for the separation of variables of the three-dimensional Dirac equation in spherical coordinates is presented. Using this approach, we consider coupling of the Dirac spinor to electromagnetic four-vector potential that satisfies the Lorentz gauge. The space components of the potential have angular (non-central) dependence such that the Dirac equation becomes separable in all coordinates. We obtain exact solutions for a class of three-parameter static electromagnetic potential whose time component is the Coulomb potential. The relativistic energy spectrum and corresponding spinor wave functions are obtained. The Aharonov–Bohm and magnetic monopole potentials are included in these solutions.     

J-matrix method of scattering in one dimension: The nonrelativistic theory

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.     

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1+1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.     

Erratum to: Series solution of a ten-parameter second-order differential equation with three regular singularities and one irregular singularity

Theoretical and Mathematical Physics -