✎ Pauli Equation [The Physics Travel Guide]

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<WRAP lag>$\left( \frac{1}{2m}(\vec \sigma ( \vec p - q\vec A))^2 + q\phi \right) \Psi = i \hbar \partial_t \Psi $</WRAP>

====== Pauli Equation:  ======

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Concrete>

The Pauli equation is the non-relativistic limit of the [[equations:dirac_equation|Dirac equation]]. 
 
<tabbox Abstract>

* Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond

The Pauli equation is the correct __non-relativistic__ equation to describe spin $1/2$ particles.

* $\Psi$ is the wave function,
  * $m$ the mass of the particle,
  * $q$ the charge of the particle,
  * $\vec{\sigma}$ the Pauli matrices,
  * $\vec{p}$ the momentum,
  * $\vec A$ the vector potential,
  * $\phi$ the electric scalar potential and
  * $\hbar$ the reduced Planck constant.

Take note that $\vec \sigma$, a "vector of matrices" is only used as a convenient short-hand notation for the sums that appear in the equation. For example, $\vec \sigma \vec p = \sigma_1 p_1 + \sigma_2 p_2 + \sigma_3 p_3.    $
</tabbox>

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