  It is known that the unrestricted Toda chain is equivalent to the Riccati
equation for the Stieltjes function of the orthogonal polynomials. Under a
special condition, this Riccati equation can be reduced to the Schr\"odinger
equation. We show that this condition is equivalent to type B solutions of the
Toda chain. We establish some nontrivial consequences arising from this
Toda-Schr\"odinger correspondence. In particular, we show that the KdV
densities can be identified with the moments of the corresponding orthogonal
polynomials. We establish equivalence between type B solutions of the Toda
molecule and the Bargmann potentials of the Schr\"odinger equation.
