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equations:pauli_equation [2017/12/04 08:01]
127.0.0.1 external edit
equations:pauli_equation [2018/04/16 09:09]
jakobadmin [Intuitive]
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-====== Pauli Equation ======+<WRAP lag>​$\left( \frac{1}{2m}(\vec \sigma ( \vec p - q\vec A))^2 + q\phi \right) \Psi i \hbar \partial_t \Psi $</​WRAP>​
  
-<tabbox Why is it interesting?> ​+====== Pauli Equation ​ ======
  
-<note tip>The Pauli equation is the correct non-relativistic equation to describe spin $1/2$ particles. ​ 
-</​note>​ 
-<tabbox Layman> ​ 
  
-<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 Student> ​ 
  
-The Pauli equation is the non-relativistic limit of the [[equations:​dirac_equation|Dirac equation]]. ​ 
-  
-<tabbox Researcher> ​ 
  
-  * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond+<tabbox Intuitive> ​
  
---> Common Question 1#+The Pauli equation describes how the state of a quantum system with [[basic_notions:​spin|half-integer spin]] changes in time.
  
 +In contrast, the [[equations:​schroedinger_equation|Schrödinger equation]] describes the time evolution of systems without spin.
 +<tabbox Concrete> ​
 +
 +The Pauli equation is the non-relativistic limit of the [[equations:​dirac_equation|Dirac equation]]. ​
    
-<--+<tabbox Abstract> ​
  
---> Common Question 2#+  * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond
  
-  
-<-- 
-  ​ 
-<tabbox Examples> ​ 
  
---Example1#+<tabbox Why is it interesting?​
  
-  +The Pauli equation is the correct __non-relativistic__ equation to describe spin $1/2$ particles. ​
-<--+
  
---Example2:#+<tabbox Definitions
  
-  +  * $\Psi$ is the wave function, 
-<-- +  * $m$ the mass of the particle, 
-   +  * $q$ the charge of the particle, 
-<tabbox History> ​+  ​* $\vec{\sigma}$ 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>​ </​tabbox>​
  
  
equations/pauli_equation.txt · Last modified: 2018/04/16 09:09 by jakobadmin