Nice one dimensional delta function

Nice one dimensional delta function - VERIFY ALL STATEMENTS...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: VERIFY ALL STATEMENTS GIVEN BELOW Consider the function f (x, α) = tanh αx . (1) The function f provides a smooth interpolation bettwen −1 and 1. In the limit α → ∞, the function f (x, α) reduces to f (x, α) = limα→∞ tanh α x = [2Θ(x) − 1] , (2) where the Heaviside function Θ(x) is the unit step function. Dirac δ -function is related to the derivative of this function. δ (x) = limα→∞ α sech2 (αx) . 2 (3) 1 ...
View Full Document

This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.

Ask a homework question - tutors are online