A Class of Discontinuities Caused by ‘Delta Functions’

1989 ◽  
pp. 305-315
Author(s):  
You-lan Zhu
Keyword(s):  
Delta Functions

scholarly journals Gravitational Interaction in the Chimney Lattice Universe

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 101
Author(s):  
Maxim Eingorn ◽  
Andrew McLaughlin ◽  
Ezgi Canay ◽  
Maksym Brilenkov ◽  
Alexander Zhuk
Keyword(s):  
Helmholtz Equation ◽  
Gravitational Potential ◽  
Fourier Expansion ◽  
Gravitational Interaction ◽  
Alternative Solution ◽  
The Third ◽  
Present Universe ◽  
Delta Functions ◽  
Yukawa Potentials ◽  
The Universe

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

Dirac Delta Functions in the Laplace‐Type Expansion of rnYlm(θ, φ)

1969 ◽  
Vol 51 (6) ◽  
pp. 2359-2362 ◽  
Author(s):  
Kenneth G. Kay ◽  
H. David Todd ◽  
Harris J. Silverstone
Keyword(s):  
Dirac Delta ◽  
Delta Functions ◽  
Laplace Type

Rotational excitations of diatomic molecule with delta potential barrier

2018 ◽  
Vol 17 (04) ◽  
pp. 1850022
Author(s):  
Sonia Lumb ◽  
Shalini Lumb ◽  
Vinod Prasad
Keyword(s):  
Diatomic Molecule ◽  
Applied Field ◽  
Morse Potential ◽  
Short Range ◽  
Delta Function ◽  
Energy Spectra ◽  
Matrix Elements ◽  
Delta Potential ◽  
Homonuclear Diatomic Molecule ◽  
Delta Functions

The interatomic interactions in a diatomic molecule can be fairly modeled by the Morse potential. Short range interactions of the molecule with the neighboring environment can be analyzed by modifying this potential by delta functions. Energy spectra and radial matrix elements have been calculated using an accurate nine-point finite-difference method for such an interacting homonuclear diatomic molecule. The effect of the strength and position of a single delta function interaction on the alignment of this molecule has been studied. The dependence of alignment on the strength of applied field has also been analyzed.

ON THE ENERGY OF A BOSE–EINSTEIN CONDENSATE IN AN OPTICAL LATTICE

2007 ◽  
Vol 19 (04) ◽  
pp. 371-384 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Optical Lattice ◽  
Critical Case ◽  
Periodic Potential ◽  
Einstein Condensate ◽  
Gamma Convergence ◽  
The Third ◽  
Bose Einstein Condensate ◽  
Delta Functions ◽  
Convergence Type ◽  
Bose Einstein

In this paper, we study the Gross–Pitaevskii energy of a Bose–Einstein condensate in the presence of an optical lattice, modeled by a periodic potential V(x3) in the third direction. We study a simple case where the wells of the potential V correspond to regions where V vanishes, and are separated by small intervals of size δ where V is large. According to the intensity of V, we determine the limiting energy as δ tends to 0. In the critical case, the periodic potential approaches a sum of delta functions and the limiting energy has a contribution due to the value of the wave function between the wells. The proof relies on Gamma convergence type techniques.

Delta Functions

2019 ◽  
pp. 557-573
Author(s):  
Kenneth B. Howell
Keyword(s):  
Delta Functions

Delta Functions

2018 ◽  
pp. 61-76
Author(s):  
Hui-Hsiung Kuo
Keyword(s):  
Delta Functions
Sign in / Sign up

Export Citation Format

Share Document