  The connection between the supersymmetric quantum mechanics involving
two-component eigenfunctions and the stability equation associated with two
classical configurations is investigated, and a matrix superpotential is
deduced. The issue of stability is ensured for the
Bogomol'nyi-Prasad-Sommerfield (BPS) states on two domain walls in a scalar
potential model containing up to fourth-order powers in the fields, which is
explicit demonstrated using the intertwining operators in terms of 2x2-matrix
superpotential in the algebraic framework of supersymmetry in quantum
mechanics. Also, a non-BPS state is found to be non-stable via fluctuation
hessian matrix.
