  We compute the quantum correction to the mass of the kink at the one-loop
level in (1+1) dimensions with minimal supersymmetry. In this paper we discuss
this issue from the Casimir energy perspective using phase shifts along with
the mode number cut-off regularization method. Exact solutions and in
particular an exact expression for the phase shifts are already available for
the bosonic sector. In this paper we derive analogous exact results for the
fermionic sector. Most importantly, we derive a unique and exact expression for
the fermionic phase shift, using the exact solutions for the continuum parts of
the spectrum and a prescription we had introduced earlier. We use the strong
and weak forms of the Levinson theorem merely for checking the consistency of
our phase shifts and results, and not as an integral part of our procedure.
Moreover, we find that the properties of the fermionic spectrum, including
bound and continuum states, are independent of the magnitude of the Yukawa
coupling constant $\lambda$, and that the dynamical mass generation occurs at
the tree level. These are all due to SUSY and are in sharp contrast to
analogous models without SUSY, such as the Jackiw-Rebbi model, where $\lambda$
is a free parameter. We use the renormalized perturbation theory and find the
counterterm which is consistent with supersymmetry. We show that this procedure
is sufficient to obtain the accepted value for the one-loop quantum correction
to the mass of the SUSY kink which is $-\frac{m}{2\pi}$.
