Related papers: Bound states for one-electron atoms in higher dime…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
Propagation effects are analyzed for electromagnetic (EM) waves which satisfy the one-soliton non-linear Schrodinger (NLS) equation in a dispersive wave guide. The coupling between momentum and frequencies due to dispersion relation is…
We find bounds on the Wilson coefficients of effective field theories (EFTs) living in a Universe undergoing expansion by requiring that its modes do not propagate further than a minimally coupled photon by a resolvable amount. To do so, we…
In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schr\"odinger equation in…
In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to…
Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass…
In the past, several efficient methods have been developed to solve the Schroedinger equation for four-nucleon bound states accurately. These are the Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis variational, the…
We show that the spectrum of the Schr\"odinger equation in two or higher dimensions does not change when Dirichlet boundary conditions are enforced on a number of isolated points inside the original domain (piercings). We have obtained the…
In this paper we first show that, there exists a precise mechanical analogue for the one-dimensional version of Schrodinger's original 4th-order, real-valued matter-wave equation. It is a composite, flexural-shear beam supported on…
We report on a result on quantum electrodynamics on a three dimensional Euclidean spacetime. The model is formulated on a toroidal lattice with unit volume and variable lattice spacing. The result is that the renormalized partition function…
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
We study hydrogen-like atoms in N=1 supersymmetric quantum electrodynamics with an electronic and a muonic family. These atoms are bound states of an anti-muon and an electron or their superpartners. The exchange of a photino converts…
We prove that Gibbs measures of nonlinear Schr\"odinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions in dimensions $d =1,2,3$. The many-body…
We analyze non-perturbatively the one-dimensional Schr\"odinger equation describing the emission of electrons from a model metal surface by a classical oscillating electric field. Placing the metal in the half-space $x\leqslant 0$, the…
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear…
We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the…
We prove the existence of a ground state of the Maxwell--Schr\"odinger equations in one spatial dimension, describing a specified amount of free charge under the influence of a fixed charge. For one case (equal free and fixed charge, i.e.,…
Results of Struwe, Grillakis, Struwe-Shatah, Kapitanski, Bahouri-Shatah, Bahouri-G\'erard and Nakanishi have established global wellposedness, regularity, and scattering in the energy class for the energy-critical nonlinear wave equation…