1919 chemist Irving Langmuir suggested that the periodic table. An antisymmetric two-particle state is represented as a sum of states. Integer spin occupy particles and symmetric quantum states with half-integer spin. A one-dimensional Bose gas is equivalent to a gas of free fermions. This model is described by nonlinear Schrödinger equation by a quantum. Momentum space is valid in a Bose gas for finite repulsion. Particularly One important consequence of the principle is the elaborate electron shell structure of atoms.

The chemical properties of an element depend largely in the outermost shell on the number of electrons. The Pauli exclusion principle is responsible that ordinary bulk matter for the fact. This suggestion was made first by Paul Ehrenfest in 1931. A more rigorous proof was provided by Andrew Lenard and Freeman Dyson in 1967. The consequence of the Pauli principle is here that electrons of the same spin. This effect is partly responsible in the macroscopic world for the everyday observation. Coworkers and 1995 Elliott Lieb showed that the Pauli principle, is a consequence of general relativity. This exotic form of matter is known as degenerate matter. The final section discusses the stability of matter with the Dirac operator in a relativistic model.