Related papers: Bound states for one-electron atoms in higher dime…
The problem of longitudinal oscillations of an electric field and a charge polarization density in QED vacuum is considered. Within the framework of semiclassical analysis, we calculate time-periodic solutions of bosonized (1+1)-dimensional…
The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the…
This paper is concerned with the Schr\"odinger equation for atoms and ions with N=1 to 10 electrons. In the asymptotic limit of large nuclear charge $Z$, we determine explicitly the low-lying energy levels and eigenstates. The asymptotic…
The Schr\"odinger equation of the spherical symmetry quantum models such as the hydrogen atom problem seems to be analytically non-solvable in higher dimensions. When we try to compactifying one or several dimensions this question can maybe…
Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in…
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schr\"odinger equation. For mass and…
In three-dimensional space an electron moving in the field of a magnetic monopole has no bound states. In this paper we explore the physics when the electron is restricted to a two-dimensional plane adjacent to a magnetic monopole. We find…
We study a 1D nonlinear Schr{\"o}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied…
In this paper, we study the existence problem of bound states of one dimensional Schrodinger system via the blow-up method.
We consider Schrodinger equations for a non-relativistic particle obeying N+1-th order higher derivative classical equation of motion. These equations are invariant under N(odd)-extended Galilean conformal (NGC) algebras in general d+1…
Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions…
We consider the nonlinear Schr{\"o}dinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power is defocusing, and the smaller power is focusing. Such a…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
Results of accurate computations of bound states in three- and four-electron atomic systems are discussed. Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state are determined from the results of…
We demonstrate that the Schr\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
We prove that standing-waves solutions to the non-linear Schr\"odinger equation in dimension one whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term $ G…
Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not…
We consider the Schr\"odinger--Poisson--Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electron field is described by the $N$-particle Schr\"odinger equation with…
We consider the Bohr correspondence limit of the Schrodinger wave function for an atomic elliptic state. We analyse this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which…