We link boundary control theory and inverse spectral theory for the Schrödinger operator $H=-\partial _{x}^{2}+q( x) $ on $L^{2}(
0,\infty) $ with Dirichlet boundary condition at $x=0.$ This provides
a shortcut to some results on inverse spectral theory due to Simon,
Gesztesy-Simon and Remling. The approach also has a clear physical
interpritation in terms of boundary control theory for the wave equation.