Quasilinearization Method and Summation of the WKB Series

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. Expansion of the $p$-th QLM iterate in powers of $\hbar$ reproduces the structure of the WKB series generating an infinite number of the WKB terms with the first $2^p$ terms reproduced exactly. The QLM quantization condition leads to exact energies for the P\"{o}schl-Teller, Hulthen, Hylleraas, Morse, Eckart potentials etc. For other, more complicated potentials the first QLM iterate, given by the closed analytic expression, is extremely accurate. The iterates converge very fast. The sixth iterate of the energy for the anharmonic oscillator and for the two-body Coulomb Dirac equation has an accuracy of 20 significant figures

Covariant Hamiltonian Dynamics with Negative Energy States

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the Point Form Relativistic Hamiltonian Dynamics. Negative energy states are introduced taking into account the restrictions imposed by a correct definition of the Poincar\'e group generators. We obtain nonpathological, manifestly covariant wave equations that dynamically contain the contributions of the negative energy states. Auxiliary negative energy states are also introduced, specially for studying the interactions of the hadronic systems with external probes.Comment: 42 pages, submitted to EPJ

Effects of Negative Energy Components in the Constituent Quark Model

Relativistic covariance requires that in the constituent quark model for mesons the positive energy states as well as the negative energy states are included. Using relativistic quasi-potential equations the contribution of the negative energy states is studied for the light and charmonium mesons. It is found that these states change the meson mass spectrum significantly but leave its global structure untouched.Comment: 14 pages revtex 3.0, 4 figures uudecoded attached in postscript format, THU-93/1