TY - JOUR
AU - Dhanuk, B. B.
AU - Pudasainee, K.
AU - Lamichhane, H. P.
AU - Adhikari, R. P.
PY - 2020/12/31
Y2 - 2024/08/08
TI - Dirac Delta Function from Closure Relation of Orthonormal Basis and its Use in Expanding Analytic Functions
JF - Journal of Nepal Physical Society
JA - J. Nep. Phys. Soc.
VL - 6
IS - 2
SE - Articles
DO - 10.3126/jnphyssoc.v6i2.34872
UR - https://www.nepjol.info/index.php/JNPhysSoc/article/view/34872
SP - 158-163
AB - <p>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 informationâ€™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 <em>log</em>(<em>x</em> + 2),<em>exp</em>(-<em>x</em><sup>2</sup>) and <em>x</em> within the valid region of arguments.</p>
ER -