Physical Deriving and Discussion of Heisenberg Uncertain Principal Through Using Schrödinger Equation and Yuji – Masanao Experiment

In this paper, authors show the process of the physical deriving of the Heisenberg Uncertainty Principal under the assumption of the wave function being a displacement function in Schrödinger Equation. This process indicates the Heisenberg Uncertainty Principal is compatible with the assumption of the wave function being a displacement function. It is found that, for a single quantum system, there exists a certainty relationship between the position x and the momentum . If the wave physical characteristics are not considered, then the product of the position and the momentum satisfies the below inequality:

≤ x
That is to say, the Heisenberg Uncertainty Principal is true. ℎ  is the reduced Plank constant. If the wave physical characteristics are considered, then the product of the position and the momentum satisfies the below inequality:
0 ≤ x <  ℎ

2

This equation provides theoretical support to Yuji Hasegawa and Masanao Ozawa Experiment. This experiment does not violate the Heisenberg Uncertainty Principal.