Dirac Delta Function from Closure Relation of Orthonormal Basis and its Use in Expanding Analytic Functions

  • B. B. Dhanuk St. Xavier’s College Maitighar, Kathmandu, Nepal
  • K. Pudasainee St. Xavier’s College Maitighar, Kathmandu, Nepal
  • H. P. Lamichhane St. Xavier’s College Maitighar, Kathmandu, Nepal
  • R. P. Adhikari Kathmandu University, Dhulekhel, Kavre, Nepal
Keywords: Dirac Delta function, Closure relation, Orthonormal basis, Generator of Dirac delta function, Analytic functions.

Abstract

One of revealing and widely used concepts in Physics and mathematics is the Dirac delta function. The Dirac delta function is a distribution on real lines which is zero everywhere except at a single point, where it is infinite. Dirac delta function has vital role in solving inhomogeneous differential equations. In addition, the Dirac delta functions can be used to explore harmonic information’s imbedded in the physical signals, various forms of Dirac delta function and can be constructed from the closure relation of orthonormal basis functions of functional space. Among many special functions, we have chosen the set of eigen functions of the Hamiltonian operator of harmonic oscillator and angular momentum operators for orthonormal basis. The closure relation of orthonormal functions  used to construct the generator of Dirac delta function which is used to expand analytic functions log(x + 2),exp(-x2) and x within the valid region of arguments.

Downloads

Download data is not yet available.
Abstract
82
pdf
65

Author Biographies

B. B. Dhanuk, St. Xavier’s College Maitighar, Kathmandu, Nepal

Department of Physics

K. Pudasainee, St. Xavier’s College Maitighar, Kathmandu, Nepal

Department of Physics

H. P. Lamichhane, St. Xavier’s College Maitighar, Kathmandu, Nepal

Department of Physics and Central Department of Physics Tribhuvan University, Kritipur, Kathmandu, Nepal

R. P. Adhikari, Kathmandu University, Dhulekhel, Kavre, Nepal

Department of Physics

Published
2020-12-31
How to Cite
Dhanuk, B., Pudasainee, K., Lamichhane, H., & Adhikari, R. (2020). Dirac Delta Function from Closure Relation of Orthonormal Basis and its Use in Expanding Analytic Functions. Journal of Nepal Physical Society, 6(2), 158-163. https://doi.org/10.3126/jnphyssoc.v6i2.34872
Section
Articles