What Exactly is Dirac’s Delta Function?

Table of Contents In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra: [tex]\delta^j_k =\left\{\begin{array}{lcl}1&\text{ if } & j=k\\0&\text{ if }&j\ne k\end{array}\right.[/tex] The key utility of the Kronecker delta is its occurrence in...