Related papers: Path integral solution for a deformed radial Rosen…
We review the integrable structure of the Dirichlet boundary problem in two dimensions. The solution to the Dirichlet boundary problem for simply-connected case is given through a quasiclassical tau-function, which satisfies the Hirota…
Path integral Monte Carlo with Green's function analysis allows the sampling of quantum mechanical properties of molecules at finite temperature. While a high-precision computation of the energy of the Born-Oppenheimer surface from path…
We show that in a special type of two-dimensional dilaton-gravity-scalar model, where both the dilaton and the scalar matter fields have noncanonical kinetic terms, it is possible to construct kink solutions whose linear perturbation…
The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state…
A new method is applied to construct an exact solution for the radiation field of a particle moving along an infinite helical trajectory. The solution is obtained in the form of a series expansion in cylindrical multipoles. The obtained…
Exact Green's functions related to Dirac particle submitted to the combination of Aharonov-Bohm and Coulomb fields in (2+1) coordinate space are analytically calculated via path integral formalism in both global and local representations.…
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined.…
Two approaches are developed for the study of the bound states of a one-dimensional Dirac equation with the potential consisting of $N$ $\delta$-function centers. One of these uses the Green's function method. This method is applicable to a…
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
We present a bi-confluent Heun potential for the Schr\"odinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to a constant. This is an infinite potential well defined on…
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…
We calculate the Green function for the Dirac equation describing a spin 1/2 particle in the presence of a potential which is a sum of the Coulomb potential V_C=-A_1/r and a Lorentz scalar potential V_S=-A_2/r. The bound state spectrum is…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
A model consisting of a Harmonic Oscillator well and a linear potential, coupled by Dirac delta function, is solved. We find the exact analytical expressions for Green's function for this problem. This Green's functions are used to…
Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…