  We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY)
symmetry transformations for the N = 2 SUSY quantum mechanical model of a one
(0 + 1)-dimensional (1D) free SUSY particle by exploiting the SUSY invariant
restrictions (SUSYIRs) on the (anti-)chiral supervariables of the SUSY theory
that is defined on a (1, 2)-dimensional supermanifold (parametrized by a
bosonic variable t and a pair of Grassmannian variables \theta and \bar\theta
with \theta^2 = \bar\theta^2 = 0, \theta\bar\theta + \bar\theta\theta = 0).
Within the framework of our novel approach, we express the Lagrangian and
conserved SUSY charges in terms of the (anti-)chiral supervariables to
demonstrate the SUSY invariance of the Lagrangian as well as the nilpotency of
the SUSY conserved charges in a simple manner. Our approach has the potential
to be generalized to the description of other N = 2 SUSY quantum mechanical
systems with physically interesting potential functions. To corroborate the
above assertion, we apply our method to derive the N = 2 continuous and
nilpotent SUSY transformations for one of the simplest interacting SUSY system
of a 1D harmonic oscillator.
