Pauli Equation [The Physics Travel Guide]

--- equations:pauli_equation [2017/10/21 15:29]
jakobadmin created
+++ equations:pauli_equation [2018/03/26 16:38]
jakobadmin
@@ Line 1: / Line 1: @@
-====== Pauli Equation ======
+====== Pauli Equation: $ \quad \left( \frac{1}{2m}(\vec \sigma ( \vec p - q\vec A))^2 + q\phi \right) \Psi = i \hbar \partial_t \Psi $ ======
 <tabbox Why is it interesting?>
-<note tip>The Pauli equation is the correct non-relativistic equation to describe spin $1/2$ particles.
+The Pauli equation is the correct __non-relativistic__ equation to describe spin $1/2$ particles.
-</note>
 <tabbox Layman>
@@ Line 19: / Line 20: @@
   * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond
---> Common Question 1#
+<tabbox Definitions>
-<--
---> Common Question 2#
+  * $\Psi$ 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,
-<tabbox Examples>
+  * $\vec A$ the vector potential,
+  * $\phi$ the electric scalar potential and
---> Example1#
+  * $\hbar$ the reduced Planck constant.
-<--
---> Example2:#
-<--
-<tabbox History>
+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>