Changes

''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.

'''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.

==Infinite Square well==

==Infinite Square well==

<math>\psi(x) = \sqrt{\frac{2}{L}}\sin{n \pi x}</math>

<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  

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:

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>

<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>

'''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

'''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>'''Azimuthal 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>'''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.

<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.