The statement you mentioned is known as the Pauli exclusion principle, which applies to fermions. The Pauli exclusion principle states that no two identical fermions can occupy the same quantum state within a quantum system simultaneously.
This principle arises from the fundamental properties of fermions and the nature of quantum mechanics. Fermions are a type of elementary particle that includes electrons, protons, and neutrons, among others. They obey a set of rules called the Fermi-Dirac statistics, which govern their behavior.
According to the Fermi-Dirac statistics, each fermion is described by a set of quantum numbers that specify its quantum state. These quantum numbers include properties like energy, momentum, and spin. Importantly, no two fermions within a system can have the exact same set of quantum numbers simultaneously.
This limitation arises due to the wave-like nature of fermions and the underlying principles of quantum mechanics. The wave function that describes a fermion must satisfy the requirement of antisymmetry, known as the Pauli principle. If two identical fermions could occupy the same quantum state, it would violate the antisymmetry of the wave function, leading to inconsistencies in the predictions of quantum mechanics.
The Pauli exclusion principle has profound consequences in many areas of physics, particularly in understanding the behavior of electrons in atoms, the formation of chemical bonds, and the properties of matter in condensed states. It is a fundamental principle that governs the behavior of fermions and plays a crucial role in shaping the structure and properties of our universe.