  In exactly solvable quantum-mechanical systems, ladder and intertwining
operators play a central role because, if they are found, the energy spectra
can be obtained algebraically. In this paper, we propose the spectral
intertwining relation as a unified relation of ladder and intertwining
operators in a way that can depend on the energy eigenvalues. It is shown that
the spectral intertwining relations can connect eigenfunctions of different
energy eigenvalues belonging to two different Hamiltonians, which cannot be
obtained by previously known structures such as shape invariance. As an
application, we find new spectral intertwining operators for the Hamiltonians
of the hydrogen atom and the Rosen--Morse potential.
