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I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as:

  1. $\delta (a x)= \frac{1}{a} \delta (x)$

  2. The derivative of $\delta (x)$

etc etc.

Such strange properties of $\delta (x)$ are mentioned in the first chapter of Arfken-Weber (7th ed.) without proof. Please suggest me a book from which I can learn the minimum essential mathematics of $\delta (x)$ function that is required to study physics. I am not looking for an advanced mathematical treatment but the book should have the proofs of the theorems stated.

Qmechanic
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Sashwat Tanay
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1 Answers1

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'Mathematical Physics' by Kusse and Westwig is just the thing you need. The fifth chapter is devoted to the Dirac-delta function. The book is fairly easy to understand and provides the proofs of the theorems that are stated in Arfken-Weber.

After having read this, you can read the appendices I and II in Cohen-Tannoudji (Quantum Mechanics) on Fourier transforms and Dirac delta functions respectively. The appendices are in Volume II of the book (the book is a pretty huge one and comes in two volumes).

Sashwat Tanay
  • 855