Fuzziness in Quantum States—Breaking through the Framework and the Principle of Quantum Mechanics

The goal of this study is to integrate fuzzy mathematics and quantum mechanics to seek deeper cosmic principles. The concept of fuzzy wave function is proposed to represent the fuzzy quantum probability by utilizing fuzzy mathematics to blur the probability (wave) of quantum mechanics. By applying the non-fuzzy formula of fuzzy quantity and the Schrödinger wave equation of quantum mechanics, the membership function equation is constructed to describe the evolution of the fuzzy wave function. The concept of membership degree amplitude is introduced to calculate fuzzy probability amplitude, and the membership degree amplitude equation is derived. Some important concepts in fuzzy mathematics are also illustrated.