The newly developed iterative method based on Green function defined by quadratures along a single trajectory is combined with the variational method to solve the ground state quantum wave function for central potentials. As an example , the method is applied to discuss the ground state solution of Yukawa potential, using Hulthen solution as the trial function.

We consider the focusing energy-critical nonlinear Schrödinger equation iut + ∆u = −|u| 4 d−2 u in dimensions d ≥ 5. We prove that if a maximal-lifespan solution u : I × Rd → C obeys supt∈I ‖∇u(t)‖2 < ‖∇W‖2, then it is global and scatters both forward and backward in time. Here W denotes the ground state, which is a stationary solution of the equation. In particular, if a solution has both ener...

We consider the focusing energy-critical nonlinear Schrödinger equation iut + ∆u = −|u| 4 d−2 u in dimensions d ≥ 5. We prove that if a maximal-lifespan solution u: I×Rd → C obeys supt∈I ‖∇u(t)‖2 < ‖∇W‖2, then it is global and scatters both forward and backward in time. Here W denotes the ground state, which is a stationary solution of the equation. In particular, if a solution has both energy ...

we assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the dirac matrices. then by making use of a suitable ansatz, the dirac equation has a very simple solution which is exact. we then have calculated the static properties of the nucleon in the ground...

in this research, structural and electronic properties of zncdn-1ten clusters (n=1-10) have been studied by formalism of density functional theory and using the projector augmented wave within local density approximation. the structural properties (such as bond length/angle and coordination number), electronic and optical properties (such as binding energy, kohn-sham spectrum and partial charge...

In this paper, we dedicate to studying the following semilinear Schrödinger system equation*...