Related papers: Static Colored SU(2) Sources in (1+1)-Dimensions -…
We consider the one-dimensional Schr\"odinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line $x\ge 0$. For this equation at fixed positive energy we give…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
We present analytically the exact energy bound-states solutions of the Schrodinger equation in $D$-dimensions for a pseudoharmonic potential plus ring-shaped potential of the form $V(r,\theta)=D_{e}(\frac{r}{% r_{e}}-\frac{r_{e}}{r})…
We consider a spinless particle moving in a random potential on a d-dimensional torus. Introducing the gradient of the logarithm of the wave-function transforms the time independent Schroedinger equation into a stochastic differential…
We investigate the relationship between the high temperature deconfined phase of the SU(2) gauge theory to the phases of the corresponding three dimensional adjoint Higgs model. For various temperatures we simulate the effective theory in a…
The vacuum dynamics of SU(2) lattice gauge theory is studied by means of a gauge-invariant effective action defined using the lattice Schr\"odinger functional. Numerical simulations are performed both at zero and finite temperature. The…
Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of…
We consider one-dimensional difference Schroedinger equations on the discrete line with a potential generated by evaluating a real-analytic potential function V(x) on the one-dimensional torus along an orbit of the shift x-->x+nw. If the…
We study the closed-string spectrum of SU(N) gauge theories in the fundamental representation in 2+1 dimensions. We calculate the energies of the lowest lying ~ 30 states using a large variety of operators characterised by the quantum…
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
The explicit, near the origin, form of the ground state of the SU(2) supermembrane matrix model is studied. We evaluate the 2nd order terms of the Taylor expansion of the wave-function, which together with the 0th and the 1st order terms…
We consider the real stationary two-dimensional Schroedinger equation. With the aid of any its particular solution we construct a Vekua equation possessing the following special property. The real parts of its solutions are solutions of the…
Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve…
We investigate coordinate independent SO(9) vector states in SU(2) Matrix theory. There are 36 vector states, and we determine what representations of SU(2) they are decomposed into. Among them we find a unique set of states transforming in…
We investigate standing waves with prescribed mass for a class of Schrodinger equations with competing Van Der Waals type potentials, arising in a model of non-relativistic bosonic atoms and molecules. By developing an approach based on a…
A slightly modified variant of the cubic periodic one-dimensional nonlinear Schroedinger equation is shown to admit weak solutions for all initial data in certain function spaces wider than L^2. These solutions depend uniformly continuously…
We present a conditionally exactly solvable singular potential for the one-dimensional Schr\"odinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general…
We present a general solution of relativistic (1+1)-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction as a function of time, uniformly in transverse space. The Khalatnikov potential is expressed as a…
We discuss the functional representation of fermions, and obtain exact expressions for wave-functionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations,…
The Newtonian character of gauge theories on a light front requires that the longitudinal momentum P^+, which plays the role of Newtonian mass, be conserved. This requirement conflicts with the standard definition of the force between two…