The one-loop eeective potential for a massive, quartically self-interacting scalar eld nonminimally coupled to gravity is calculated in a Bianchi I universe with small anisotropy. The kernel of a Schrr odinger-like equation is found, and its coincidence limit used to obtain the determinant of the Klein-Gordon operator. The eeects of the anisotropy on symmetry breaking and the viability of new i...

The role of edge states in phenomena like the quantum Hall eeect is well known. In this paper we show how the choice of boundary conditions for a one-particle Schrr odinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic eld. In each case, edge states arise from a non-...

The divergent Rayleigh-Schrr odinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are generalized Pad e approximants that are obtained from an algebraic equation of arbitrary degree. Numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence o...

One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The transition and re ection amplitudes are expressed in terms of two complex functions of the incident energy, which are similar to the Jost function in the partial...

This paper is concerned with the existence and qualitative property of standing wave solutions (t; x) = e ?iEt=~ v(x) for the nonlinear Schrr odinger equation ~ @ @t + ~ 2 2 ? V (x) + jj p?1 = 0 with E being a critical frequency in the sense that min R N V (x) = E. We show that there exists a standing wave which is trapped in a neighborhood of isolated minimum points of V and whose amplitude go...

We show that light scalars can form quasibound states around binaries. In the nonrelativistic regime, these are formally described by quantum-mechanical Schr\"odinger equation for a one-electron heteronuclear diatomic molecule. performed extensive numerical simulations of scalar fields black hole binaries, showing structure condenses binary---we dub ``gravitational molecules.'' further well per...

An impermeable barrier at $r=r_{cl}$ in the effective potential of relativistic Schr\"odinger-type equation leads to exclusion range $0 \leq r < r_{cl}$ from wave function domain. Based on duality and Dirac equation, a similar should be made functions domain equation. As result, we obtain new solutions Coulomb repulsive field. Calculations show that depending working parameters, distances sever...

Schr\"odinger equation is a nonrelativistic wave equation, which does not have Lorentz invariance. Therefore, this has large theoretical error in the precise calculation of hydrogen-like system. So commonly used method Dirac-Hartree-Fock approximation atomic However, we found new eigen whose eigenvalue system approximates quantum electrodynamics. Hence, propose scheme for hyperfine structure ba...

We integrate the one-dimensional nonlinear Schrr odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering oo an interface separating two regions of constant potential modeled by a linear ramp. Transmission coeecients and inelasticities are computed as functions of the potential diierence and the slope of the ramp. Our data show that the ram...

Recent scanning tunneling microscopy (STM) studies on the (111) faces of noble metals have directly imaged electronic surface-connned states, and dramatic standing-wave patterns have been observed in geometrically arranged \quantum corral" structures formed by Fe adatoms on Cu(111). We present a coherent elastic scattering theory for the electronic states in these \leaky" connning structures by...