Related papers: Delta potentials revisited via Fourier transform
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…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has…
The problem of quantum particle moving in Dirac delta potential with instant changing well depth is studied by using formalism of tomographic representation of quantum mechanics.The bound state tomogram is given in terms of error…
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.…
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…
The resonant transmission of a moving particle which interacts with an one-dimensional array of N delta-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the…
A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a…
We consider the nonlinear Schr\"{o}dinger equation with a repulsive Dirac delta potential in one dimensional Euclidean space. We classify the global dynamics of even solutions with the same action as the high-frequency ground state standing…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
We use two renormalization techniques, Effective Field Theory and the Similarity Renormalization Group, to solve simple Schr{\"o}dinger equations with delta-function potentials in one and two dimensions. The familiar one-dimensional…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…
In this paper we derive an expression for the dynamic electric polarizability of a particle bound by a double delta potential for frequencies below and above the absolute value of the particle's ground state energy. The derived expression…
Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by the incorporation of the self-adjoint extension method to the path integral formalism. The energy-dependent Green functions for free particle plus…
We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical…
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed and the results are compared with the one using the standard partial wave analysis developed for…
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…