GENERALIZED FOURIER-GRID HAMILTONIAN APPROACH TO THE DIRAC-EQUATION - VARIATIONAL SOLUTION WITHOUT BASIS SET

A variational procedure without the need of using L2 basis set expansion or trial wave functions is introduced for efficient and accurate treatment of relativistic quantum-mechanical eigenvalue problems. The method, based on the extension of the Fourier-grid Hamiltonian technique, is free from the problems of variational collapse, Further, the procedure does not require the computation of potential matrix elements and the eigenvectors provide directly the amplitude of wave functions at the space grid points. The simplicity and accuracy of the method is illustrated for a case study of the Dirac-Coulomb-field equation.