2
votes
1answer
98 views

Fourier integral form of the delta function?

I'm learning basic maths for physicist and was wondering what do we use the Dirac delta function for? What is the difference between "the Fourier integral form" and the usual way of expressing the ...
1
vote
1answer
44 views

How do you handle a functional input in a Dirac delta function and prove these types of relations?

I have a quadratic relation inside of a Dirac delta function with the following relation \begin{align} \delta((x-x_1)(x-x_2)) = \dfrac{ \delta(x-x_1) + \delta(x-x_2) }{|x_1-x_2|}. \end{align} How do ...
3
votes
3answers
208 views

The Dirac-Delta function as an initial state for the quantum free particle

I want to ask if it is reasonable that I use the Dirac-Delta function as an intial state ($\Psi (x,0) $) for the free particle wavefunction and interpret it such that I say that the particle is ...