  The spectral problem $(A + V(z))\psi=z\psi$ is considered with $A$, a
self-adjoint Hamiltonian of sufficiently arbitrary nature. The perturbation
$V(z)$ is assumed to depend on the energy $z$ as resolvent of another
self-adjoint operator $A':$ $V(z)=-B(A'-z)^{-1}B^{*}$. It is supposed that
operator $B$ has a finite Hilbert-Schmidt norm and spectra of operators $A$ and
$A'$ are separated. The conditions are formulated when the perturbation $V(z)$
may be replaced with an energy-independent ``potential'' $W$ such that the
Hamiltonian $H=A +W$ has the same spectrum (more exactly a part of spectrum)
and the same eigenfunctions as the initial spectral problem. The orthogonality
and expansion theorems are proved for eigenfunction systems of the Hamiltonian
$ H=A + W $. Scattering theory is developed for $H$ in the case when operator
$A$ has continuous spectrum. Applications of the results obtained to few-body
problems are discussed.
