# Delta functions live under integral signs, and two expressions (D 1 (x) and D 2 (x)) involving delta functions are said to be equal if for every (ordinary) function f(x).(a) Show that where c is a real constant. (Be sure to check the case where c is negative.)(b) Let (x) be the step function: (In the rare case where

Chapter 2, Problems #23

Delta functions live under integral signs, and two expressions (D_{1}(x) and D_{2} (x)) involving delta functions are said to be equal if

for every (ordinary) function f(x).

(a) Show that

where c is a real constant. (Be sure to check the case where c is negative.)

(b) Let θ (x) be the step function:

(In the rare case where it actually matters, we define θ (0) to be 1/2.) Show that dθ/dx = δ(x).

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**Related Book For**

## Introduction To Quantum Mechanics

3rd Edition

Authors: David J. Griffiths, Darrell F. Schroeter

ISBN: 9781107189638