  We propose a simple procedure to produce energy eigenstates of a Hamiltonian
with discrete eigenvalues. We use ancilla qubits and quantum entanglement to
separate an energy eigenstate from the other energy eigenstates. We exhibit a
few examples derived from the (1+1)-dimensional massless Schwinger model. Our
procedure in principle will be applicable for a Hamiltonian with a finite
dimensional Hilbert space. Choosing an initial state properly, we can in
principle produce any energy eigenstate of the Hamiltonian.
