Related papers: Quadratic supersymmetric transformations of the Di…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. It has been a long standing problem on what are other…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
We establish a local Harnack inequality in a neighborhood of an indecomposable singular point of a stationary integral varifold. Extending the method of Gr\"uter and Widman \cite{gruter1982green}, we construct the Green function on a…
It is shown that boundary conditions of the Darboux transformed Dirac Sturm--Liouville problem are always zero-valued independently on boundary conditions of initial problem.
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with…
We consider the Dirac equation in 1+1 space-time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant.…
We define B\"acklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on…
This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\"odinger equation, specially the integrable cases in…
The resolvent of supersymmetric Dirac Hamiltonian is studied in detail. Due to supersymmetry the squared Dirac Hamiltonian becomes block-diagonal whose elements are in essence non-relativistic Schr\"odinger-type Hamiltonians. This enables…
It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using…
Using Darboux transformation one can construct infinite family of potentials which lead to the flat spectrum of scalar field fluctuations with arbitrary multiple precision, and, at the same time, with "essentially blue" spectrum of…
The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical…
A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the…
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the…
In 1984, the second author conjectured a quadratic transformation formula which relates two hypergeometric 2F1 functions over a finite field F_q. We prove this conjecture and give an application. The proof depends on a new linear…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral…
We make a detailed study of the first and second-order SUSY partners of a one-dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the second-order transformations increase the…