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Let me reassure you -- your understanding of the Pauli Exclusion Principle is not quite correct. Two electrons at opposite ends of the solar system are quite free to have the same energy. The Pauli Exclusion Principle applies only to stationary states of electrons, or to electrons bound within the same atom, molecule, or neighbourhood. What the Pauli Exclusion Principle is REALLY saying, in practical terms, is that you can only have a maximum of 2 electrons in the same place at the same time, and those two must have opposite spin. Electrons are in the family of particles known as fermions, which obey a set of rules known as Fermi-Dirac Statistics.The Pauli Exclusion Principle is usually applied in the context of atomic structure or chemical bonding in molecules, and solutions to the Time-Independent Schrödinger Equation. In the context of atomic structure it helps to explain the capacity of the various electron shells and sub-shells. An electron in an atom, in the single-electron wavefunction approximation, is assigned a set of 4 quantum numbers: n which is the main contributor to the energy of the electron in an atom, and to its average distance from the nucleus. It is a positive integer.l which determines the shape of a wavefunction. It is also an integer, and may range from 0 (spherical) to n-1, and can also affect the energy of a multiple electron atom.ml determines the orientation of the wavefunction. It takes integer values between –l and +l .It does not affect the energy.ms takes a value of either –1/2 or +1/2.So, to take an example, if we think of a sodium atom which has 11 electrons, each of those electrons in the atom has to have a different set of quantum numbers.The first two go to the lowest energy shell: with quantum number sets (1,0,0,–) and (1,0,0,+). There are no other possibilities for the lowest energy shell. The next two go to a higher energy subshell with quantum number sets (2,0,0,–) and (2,0,0,+), and then six more can be accommodated in a slightly higher energy subshell (2,1,–1,–), (2,1,–1,+), (2,1,0,–), (2,1,0,+), (2,1,1,–), and (2,1,1,+). In an isolated atom these six all have the same energy. Finally, the 11th electron has no more possibilities with n=2, so it must go to the higher energy shell with n=3, where it sits all alone with the quantum number set (3,0,0,–). That is why sodium loses an electron so readily, and why the chemistry of sodium is dominated by the positive sodium ion with only 10 electrons.There is a problem, an unresolved one, relating to quantum particles and faster-than-light communication. It comes under the umbrella of "quantum entanglement", and there is a wikipedia article that will provide a reasonable introduction if you want to follow that up.
Interesting SoulSurfer And then we get to 'especially if they have different non-interacting symmetries.' Damocles )Symmetries are weird phenomena.
Approximations of chemical interactions? As for symmetries I don't think we have anyone here really able to express it any better Do you find a lot of difference between the way physics describe it and chemistry?==I really like Stanford university. ...sorry, you cannot view external links. To see them, please
REGISTER or LOGINI will follow that with an allegory (hopefully I will manage to keep it short) that is a metaphor for molecular structure:Once upon a time, in a parallel universe, the Nyankis family took advantage of the latest genetic engineering techniques to produce a clone of a dozen children who were very athletically gifted. When they went to school, they took up baseball, and were remarkably successful. In early adulthood they formed their own Nyankis baseball team, which won the World Series 5 years in a row.When they took the field they had some unusual features about the way they would play. The commentators were unable to distinguish the individual family members, and as they were all equally talented in all roles, they liked to frequently change places around the field -- several times in an inning! (This was partly to escape boredom and partly to confuse the opposition).Some physicists and some chemists were called upon to analyse the play style and the singular success of this team. The physicists' first approach to this problem was to consider the family as a whole and the interactions within it, and to analyse the symmetries of their peculiar style of play. The chemists, on the other hand, wanted to start from issues like how the pitcher, the short stop, and the first baseman used to co-operate to frequently make double-plays (regardless of who was temporarily occupying those field positions).