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What are quantum numbers and how do I use them?

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What are quantum numbers and how do I use them?

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A quantum number describes the energies of electrons in atoms. Each quantum number specifies the value of a conserved quantity in the dynamics of the quantum system. Since any quantum system can have one or more quantum numbers, it is a futile job to list all possible quantum numbers. The most widely studied set of quantum numbers is that for a single electron in an atom: not only because it is useful in chemistry, being the basic notion behind the periodic table, valence (chemistry) and a host of other properties, but also because it is a solvable and realistic problem, and, as such, finds widespread use in textbooks. In non-relativistic quantum mechanics the Hamiltonian of this system consists of the kinetic energy of the electron and the potential energy due to the Coulomb force between the nucleus and the electron. The kinetic energy can be separated into a piece which is due to angular momentum, J, of the electron around the nucleus, and the remainder. Since the potential is spher

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