Alternative solution of delta–function potential by green functions and renormalization

Abstract

Simple technique of constructing the Green’s function that is associated with the Hamiltonian, H  Ho  (x) is presented.
The result was applied in a case where Ho is the Hamiltonian of a free particle in given R dimensions. The theoretical concepts of
field such as regularization and renomalization was introduced in order to handle the case at infinity which characterized the
formal Green’s function for R  2. A comparison was also made with alternative derivation using time –independent Schrodinger
equation for a particle in potential, V (x) (x)  .