  The construction of Dirac delta type potentials has been achieved with the
use of the theory of self adjoint extensions of non-self adjoint formally
Hermitian (symmetric) operators. The application of this formalism to
investigate the possible self adjoint extensions of the one dimensional
kinematic operator $K=-d^2/dx^2$ on the infinite square well potential is quite
illustrative and has been given elsewhere. This requires the definition and use
of four independent real parameters, which relate the boundary values of the
wave functions at the walls. By means of a different approach, that fixes
matching conditions at the origin for the wave functions, it is possible to
define a perturbation of the type $a\delta(x)+b\delta'(x)$, thus depending on
two parameters, on the infinite square well. The objective of this paper is to
investigate whether these two approaches are compatible in the sense that
perturbations like $a\delta(x)+b\delta'(x)$ can be fixed and determined using
the first approach.
