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Added example of infinite square well and some more explanation
''Quantum numbers'' are the set of four parametres given to an [[electron]] attached to an atom which describe the characteristics of its movement. The [[Pauli exclusion principle]] states that no electron can have the same four quantum numbers.
''Quantum numbers'' are sets of parameters that produce physically acceptable solutions to the [[Schrodinger equation]]. They often take [[integer]] or half-integer values. They are used to label the different eigenstates of a quantum system. The number of quantum numbers in a system depends on the system, but there will be equal to or greater than the number of dimensions in the problem.
'''Principle quantum number''' - corresponds to the main [[electron shell]] in which the electron resides. Can have the value n=1, 2, 3 up to 7 corresponding to shells with increasing amounts of energy
=Infinite Square well=
<br>'''Azmuthal quantum number''' - corresponds to the [[electron subshell]] of the electron. Can have the number l=1, 2, 3 up to n-1
The problem of an [[Schrodinger_equation#Free_particle_in_one_dimension|infinite square well]] demonstrates quantum numbers. For a one dimensional box, the possible eigenstates (states in which the we might find the system in when we make a measurement of it) are:
<br>'''Magnetic quantum number''' - corresponds to the orbital of the electron, the orbital is the different orientations of the electron subshell around the atom
<br>'''Spin quantum number''' - corresponds to the spin of the electron, can have the value 1/2 or -1/2, indicating that each orbital of an atom can only hold 2 electrons
<math>\psi(x) = \sqrt{\frac{2}{L}}\sin{n \pi x}</math>
Here, <math>n</math> is our quantum number and can take integer values. Notice how in this 1 dimensional problem there is only 1 quantum number. The
infinite square well problem can be extended to consider a particle trapped inside a 3 dimensional box. This produces a solution of the form:
<math>\psi(x,y,z) = \sqrt{\frac{8}{L_x L_y L_z}} \sin{(n_x x)} \sin{(n_y y)} \sin{(n_z z)}</math>
where <math>L_x</math>, <math>L_y</math> and <math>L_z</math> are the lengths of each side of the box. Now that we are working in three dimensions, the number of quantum numbers has increased to 3. They are: <math>n_x</math>, <math>n_y</math>, <math>n_z</math> and again take integer values.
=The Hydrogen Atom=
Four quantum numbers are required to describe the state of an [[electron]] in a [[hydrogen]] atom. As the electron is a [[fermion]], the [[Pauli exclusion principle]] applies and states that no electron can have the same four quantum numbers. The four quantum numbers are:
'''Principle quantum number''' - corresponds to the main [[electron shell]] in which the electron resides. Can have the value n=1, 2, 3..., corresponding to shells with increasing amounts of energy. However in stable atoms, this tends to be less than or equal to 7
<br>'''Azmuthal quantum number''' - corresponds to the [[electron subshell]] of the electron. Can have the number l=0, 1, 2, 3 up to n-1. It is also sometimes called the "angular momentum quantum number", due to its relationship with [[angular momentum]]
<br>'''Magnetic quantum number''' - corresponds to the [[orbital]] of the electron, the orbital is the different orientations of the electron subshell around the atom. It is normally denoted by m and varies from -l to l, taking integer values, i.e. -1, -l + 1,..., -1, 0, 1, ..., l-1, l
<br>'''Spin quantum number''' - corresponds to the spin of the electron, can have the value 1/2 or -1/2, indicating that each orbital of an atom can only hold 2 electrons. This is an example of a quantum number that takes half-integer values.
Although this is an example with three dimensions, there are 4 quantum numbers due to spin. Considering the electron as a planet orbiting the proton can be a useful analogy to understand spin. In this analogy, the angular momentum of a [[planet]] about the sun corresponds the azmuthal quantum number and the rotation of the planet about its axis to spin. However the analogy is not perfect; an electron is a point particle and therefore it makes no sense for it to rotate about its own axis. Instead the electron is said to have an intrinsic angular momentum.
==See also==
==See also==