Abstract
In this paper, based on the discussion on what the real state of a coin at each point should be, we propose two basic assumptions. Then we point out the mathematical foundations that these two assumptions rely on and the familiar physical principles which these two assumptions, respectively, correspond to. These two assumptions, as required, do not seek help from the well-known formulation of quantum mechanics. They are self-consistent in a new presentation. Based on two basic assumptions, we derive the real state in a simple way and claim that the real state equals the quantum state totally after comparison from different aspects. We thus prove that the quantum state is the ontological object which obeys the redefinition of the reality rather than just a vague concept in quantum theory. We also consider the way in which Born's rule arises naturally.
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