DiracVerteilung

DiracVerteilung refers to the Dirac delta function, a generalized function introduced by physicist Paul Dirac. It is a mathematical construct that is zero everywhere except at a single point, where it is infinitely large. Despite its seemingly paradoxical nature, the Dirac delta function is incredibly useful in various fields of physics and engineering. Its key characteristic is that its integral over any interval containing the point of singularity is equal to 1. This property makes it ideal for representing impulses or concentrated sources. For example, in classical mechanics, it can describe a perfectly instantaneous force. In quantum mechanics, it is used to represent point particles or states with definite positions. Mathematically, the Dirac delta function is often approximated by a sequence of functions that become increasingly peaked at a single point while maintaining a unit area. Common examples include the normalized Gaussian function or the sinc function as they approach zero width. It is fundamental in signal processing for sampling theory and in solving differential equations. The Dirac delta function is not a function in the traditional sense but a distribution, meaning it is defined by its action on other functions. Its introduction by Dirac revolutionized the way physicists handled concepts involving localized phenomena.