Countable infinity of isospectral potential families

Given any one-dimensional potential V(x) with n bound states, we construct an infinite number of isospectral potential families $V^{\left(a\right)}$(${\lambda }_0$,${\lambda }_1$,..., ${\lambda }_{n-1}$;x). The parameter a takes integer values and the n parameters ${\lambda }_i$ take real continuous values. All potentials have identical bound-state eigenvalues, but the reflection and transmission coefficients depend on the index a.