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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 ...
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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.
- Spring '09