  There are hamiltonians that solve a search problem of finding one of $N$
items in $O(\sqrt{N})$ steps. They are hamiltonians to describe an oscillation
between two states. In this paper we propose a generalized search hamiltonian,
$H_{g}$. Then the known search hamiltonians become special cases of $H_{g}$.
  From the generalized search hamiltonian, we present remarkable results that
searching with 100% is subject only to the phase factor in $H_{g}$ and
independent to the number of states or initialization.

Quantum Physics