Question

Dirac Delta Function

Prove Prove f{$(x)} = Lim F {f, cos} : no

Answer 1

The Dirac delta function, 8x) is definest and Called a generalized fumetion on distribution This leads to the result for a point particle that can be considered on the limit of Sequence, for example; In(x)= n e men=1,2,3, So, Sn to as n & for any nzo Also, In 10 dn=1 and lim (Sn D du = (860) dn = 1 so, delta function can be considered as the Ilmit of sequence of ordinary functions and We cosité, 80= lim un è me As a distribution, the Dinac delta function is a linear functional that maps every function to its value at zero. The kronechen delta finetion, which is usually defined on a discrete domain and takes values o and I is a discrete analog of the Dirac delta formation, ta ; azo 50, 8(n) = 9 to into a which is also satisfy 1 god che = 1

fumetion The fourier tromform of the Drac Delter IS F480) = 2 kn god de N1 so', F{sen)} = lim {fu (w)} = 1/2