  We investigate the relation between time-dependent Hartree-Fock (TDHF) states
and the adiabatic eigenstates by constructing a boost-invariant single-particle
Hamiltonian. The method is numerically realized within a full three-dimensional
TDHF which includes all the terms of the Skyrme energy functional and without
any symmetry restrictions. The study of a free translational motion of a
nucleus demonstrates the validity of the concept of boost-invariant and
adiabatic TDHF states. The interpretation is further corroborated by the test
case of fusion of $^{16}{\textrm O}$+$^{16}{\textrm O}$. As a first
application, we present a study of the nuclear Landau-Zener effect on a
collision of $^{4}{\textrm {He}}$+$^{16}{\textrm O}$.
