Dongfang Special Entangled Solution of Schrödinger Hydrogen Equation

The textbook solutions of Schrödinger equations are usually represented as the combination of multiple special function symbols, resulting in a large number of missing exact solutions not being discovered. Taking the Schrödinger wave function of a hydrogen atom as an example, regressing to the analytical expression that can be extended and programmed for testing, two types of special entangled wave functions that have not been described by established theories have been discovered. Specifically, when the magnetic quantum number is 0, the traditional Schrödinger wave function degenerates into a binary function about radial variables r and angle θ without angles φ. The conclusion of this reasoning process, which seems very rigorous in the traditional sense, is actually extremely untrue. The Schrödinger equation for hydrogen atoms has two types of special entangled solutions with magnetic quantum numbers of 0, and the sine and cosine functions of angle φ are included in it, implying that there are other unknown wave functions that satisfy the Schrödinger equation and even affect the energy eigenvalue formula. The three-dimensional function image of the special entangled solution of the hydrogen atom Schrödinger equation is further drawn. The results show intuitively and clearly that there is no one-to-one correspondence between the zero or extreme point of the modulus function of the ternary function and that of the square of the modulus function of the ternary function. It is concluded that the definition of the square of the wave function modulus as the probability density function lacks causality, and it is an urgent problem to derive the probability density function according to the basic principle.