Pauli exclusion principle 

The Pauli principle only applies to fermions, particles which form antisymmetric quantum states and have half-integer spin. Fermions include protons, neutrons, and electrons, the three types of elementary particles which constitute ordinary matter. The Pauli exclusion principle governs many of the distinctive characteristics of matter. Particles like the photon and graviton do not obey the Pauli exclusion principle, because they are bosons (i.e. they form symmetric quantum states and have integer spin) rather than fermions.

Based on the article on identical particles, the Pauli principle can be easily derived. Fermions of the same species form totally antisymmetric states, which in the two-particle case means that

<math> |\psi \psi'\rangle = - |\psi'\psi\rangle </math>

If both particles occupy the quantum state |ψ>, the state of the entire system is |ψψ>. Then

<math> |\psi\psi\rangle = - |\psi\psi\rangle = 0 \; \hbox{(zero ket)} </math>

so such a state doesn't occur. This is readily generalizable to the case of more than two particles.

Consequences

The Pauli exclusion principle plays a role in a huge number of physical phenomena. One of the most important, and the one for which it was originally formulated, is the electron shell structure of atoms. An electrically neutral atom contains bound electrons equal in number to the protons in the nucleus. Since electrons are fermions, the Pauli exclusion principle forbids them from occupying the same quantum state.

For example, consider a neutral helium atom, which has two bound electrons. Both of these electrons can occupy the lowest-energy (1s) states by acquiring opposite spin. This doesn't violate the Pauli principle because spin is part of the quantum state of the electron, so the two electrons are occupying different quantum states. However, the spin can take only two different values (or eigenvalues.) In a lithium atom, which contains three bound electrons, the third electron cannot fit into a 1s state, and has to occupy one of the higher-energy 2s states instead. Similarly, successive elements produce successively higher-energy shells. The chemical properties of an element largely depends on the number of electrons in the outermost shell, which gives rise to the periodic table of the elements.

The Pauli principle is also responsible for the large-scale stability of matter. Molecules cannot be pushed arbitrarily close together, because the bound electrons in each molecule are forbidden from entering the same state as the electrons in the other molecules - this is the reason for the repulsive r^-12 term in the Lennard-Jones potential. The Pauli principle is the reason you do not fall through the floor.

Astronomy provides the most spectacular demonstrations of this effect, in the form of white dwarf stars and neutron stars. In both types of objects, the usual atomic structures are disrupted by large gravitational forces, leaving the constituents supported only by a "degeneracy pressure" produced by the Pauli exclusion principle. This exotic form of matter is known as degenerate matter. In white dwarfs, the atoms are held apart by the degeneracy pressure of the electrons. In neutron stars, which exhibit even larger gravitational forces, the electrons have merged with the protons to form neutrons, which produce a larger degeneracy pressure.

that we shall pay any price, bear any burden, meet any hardship, the success of liberty. This much we pledge. . .and more. To those old allies whose cultural and spiritual origins we share: little we cannot do in a host of co-operative ventures. a powerful challenge, at odds, and split asunder. we pledge our word that one form of colonial control shall not We shall not always expect to find them supporting our view. own freedom. . .and to remember that. . .in the past. . .those who To those people in the huts and villages of half the globe efforts to help them help themselves, for whatever period not because we seek their votes, but because it is right. it cannot save the few who are rich. To our sister republics south of our border: we offer a special pledge. . . . . .to assist free men and free governments in casting off the chains of hostile powers. Let all our neighbors know that we shall join with them every other power know that this hemisphere intends to remain the master our last best hope in an age where the instruments of war of support. . .to prevent it from becoming merely a forum for and to enlarge the area in which its writ may run. Finally, to those nations who would make themselves our adversaries, the quest for peace; before the dark powers of destruction unleashed We dare not tempt them with weakness. For only when our arms are sufficient But neither can two great and powerful groups of nations take comfort from both rightly alarmed by the steady spread of the deadly atom, yet both racing .

 On wordlookup.net  

All is still licensed under the GNU FDL.
It uses material from the wikipedia.