Related papers: Delta function singularity in the Reduction of Rad…
By careful exploration of separation of variables into the Laplacian in spherical coordinates, we obtain the extra delta-like singularity, elimination of which restricts the radial wave function at the origin. This constraint has the form…
By careful exploration of separation of variables into the Laplacian in spherical coordinates, we obtain the extra delta-like singularity, elimination of which restricts the radial wave function at the origin. This constraint has the form…
There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin,…
Careful exploration of the idea that equation for radial wave function must be compatible with the full Schrodinger equation shows appearance of the delta-function while reduction of full Schrodinger equation in spherical coordinates.…
Singular behavior of the Laplace operator in spherical coordinates is investigated. It is shown that in course of transition to the reduced radial wave function in the Schrodinger equation there appears additional term consisting the Dirac…
We revisit a recent discussion about the boundary condition at the origin in the Schroedinger radial equation for central potentials. Using a slight modification of the usual spherical coordinates, the origin of a previously reported Dirac…
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…
We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin.…
We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of…
Exploring the idea that equation for radial wave function must be compatible with the full Schrodinger equation, a boundary condition is derived.
In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…
We obtain bounds for the Faltings's delta function for any Riemann surface of genus greater than one. The bounds are in terms of the genus of the surface and two basic quantities coming from hyperbolic geometry: The length of the shortest…
We give one more proof in two and three space dimensions that the irregular solution of the Schrodinger equation, for zero angular momentum, is in fact the solution of an equation containing an extra 'delta function'. We propose another…
We show that additional solutions must be ignored (in differences of the Schrodinger and Klein-Gordon equations) in the Dirac equation, where usually passed the second order radial equation, called the reduced equation, instead of a system.…
Making an ansatz to the wave function, the exact solutions of the $D$% -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the…
A superspace version of the Schr\"odinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is…
We investigate the existence and the singular structure of delta wave solutions to a semilinear strictly hyperbolic equation with strongly singular initial and boundary conditions. The boundary conditions are given in nonlocal form with a…
Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded obstacle…
Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive…
We study the relativistic version of Schr\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states.…