For the problem-solving in the state-space, this article investigates the effectiveness of the method which makes use of quantum mechanics. First this article restricts the state-space to vector-space, and shows that quantum mechanics has more general property than state-space approach in the vector space. For the general problem, this article then fromalizes the relation of between problem and solution by the method of quantum mechanics, and provides the urgent subject. Finally, this article provides the laws which exist under the conditions of linearity and Hermiticity, and investigates for the key to the next step.