Editing Spin quantum number (section)

== Relation to spin vectors ==
For a solution of either the nonrelativistic [[Pauli equation]] or the relativistic [[Dirac equation]], the quantized angular momentum (see [[angular momentum quantum number]]) can be written as:
<math display="block"> \Vert \mathbf{s} \Vert = \sqrt{s \, (s+1)\,} \, \hbar</math>
where
* <math>\mathbf{s}</math> is the quantized [[spin vector]] or spinor
* <math>\Vert \mathbf{s}\Vert</math> is the [[norm (mathematics)|norm]] of the spin vector
* {{mvar|s}} is the spin quantum number associated with the spin angular momentum
* <math>\hbar</math> is the [[reduced Planck constant]].

Given an arbitrary direction {{mvar|z}} (usually determined by an external magnetic field) the spin {{mvar|z}}-projection is given by
:<math>s_z = m_s \, \hbar</math>

where {{mvar|m{{sub|s}}}} is the '''magnetic spin quantum number''', ranging from −{{mvar|s}} to +{{mvar|s}} in steps of one. This generates {{math| 2 {{mvar|s}} + 1 }} different values of {{mvar|m{{sub|s}}}}.

The allowed values for {{mvar|s}} are non-negative [[integer]]s or [[half-integer]]s. [[Fermion]]s have half-integer values, including the [[electron]], [[proton]] and [[neutron]] which all have {{nobr| {{mvar|s}} {{=}} {{sfrac|+| 1 |2}} .}} [[Boson]]s such as the [[photon]] and all [[meson]]s) have integer spin values.