Hamiltonian and measuring time for analog quantum search

We derive in this study a Hamiltonian to solve with certainty the analog quantum search problem analogue to the Grover algorithm. The general form of the initial state is considered. Since the evaluation of the measuring time for finding the marked state by probability of unity is crucially important in the problem, especially when the Bohr frequency is high, we then give the exact formula as a function of all given parameters for the measuring time.