  It is shown that bound state solutions of the one dimensional Bogoliubov-de
Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on
the space coordinate. The existence of bound states in continuum (BIC) like
solutions has also been confirmed both in the normal phase as well as in the
super-conducting phase. We also show that a combination of Fermi velocity and
gap parameter step-like profiles provides scattering solutions with normal
reflection and transmission.
