Before revision: Based on the behavior coordinate system, ideal individual model and quantum probability, the state of an ideal individual is assumed to be described by the behavior state function. Then we present a conjecture that the ideal individuals can be identical. A consequence of the identical individual conjecture is that the existence of the personal space and the behavior differentiation under high population density condition receive a possible theoretical explanation .
After revision: The identical ideal individual hypothesis is proposed. According to this hypothesis, the identical ideal individuals should be classified into two classes: the bosonic individuals and the fermionic individuals. The bosonic individuals can occupy the same behavior state while the fermionic individuals can not be in the same behavior state. We propose that human beings and many species of animals are fermionic, which can not occupy the same behavior state according to the Pauli exclusion principle. An unified theoretical explanation is given for the natures of two important and seemingly irrelated phenomena in psychology: the existence of the personal space and the behavior differentiation under high population density condition receive a possible theoretical explanation .