User Tools

Site Tools


equations:pauli_equation

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
equations:pauli_equation [2018/03/13 11:12]
jakobadmin
equations:pauli_equation [2018/04/16 09:09]
jakobadmin [Intuitive]
Line 1: Line 1:
-====== 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>​
  
-<note tip>$$ \left( \frac{1}{2m}(\vec \sigma ( \vec p - q\vec A))^2 + q\phi \right) \Psi i \hbar \partial_t \Psi $$ +====== Pauli Equation ​ ======
--->​Definitions # +
-$\Psi$ 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 and $\phi$ the electric scalar potential. ​+
  
-Take note that $\vec \sigma$ is only 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.    $ 
-<-- 
-</​note>​ 
  
  
-<tabbox Why is it interesting?> ​ 
  
-The Pauli equation is the correct non-relativistic equation to describe spin $1/2$ particles. ​+<tabbox Intuitive> ​
  
-<tabbox Layman> ​+The Pauli equation describes how the state of a quantum system with [[basic_notions:​spin|half-integer spin]] changes in time.
  
-<note tip> +In contrastthe [[equations:​schroedinger_equation|Schrödinger equation]] describes the time evolution of systems without spin
-Explanations in this section should contain no formulasbut instead colloquial things like you would hear them during a coffee break or at a cocktail party. +<​tabbox ​Concrete
-</​note>​ +
-  ​ +
-<​tabbox ​Student+
  
 The Pauli equation is the non-relativistic limit of the [[equations:​dirac_equation|Dirac equation]]. ​ The Pauli equation is the non-relativistic limit of the [[equations:​dirac_equation|Dirac equation]]. ​
    
-<​tabbox ​Researcher+<​tabbox ​Abstract
  
   * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond   * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond
  
---> Common Question 1# 
  
-  +<tabbox Why is it interesting?> ​
-<--+
  
---> Common Question ​2#+The Pauli equation is the correct __non-relativistic__ equation to describe spin $1/2$ particles. ​
  
-  +<​tabbox ​Definitions
-<-- +
-   +
-<​tabbox ​Examples+
  
---> Example1# +  * $\Psi$ 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, 
---> Example2:#​ +  * $\vec A$ the vector potential, 
- +  ​* $\phi$ the electric scalar potential and 
-  +  * $\hbar$ the reduced Planck constant.
-<-- +
-   +
-<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>​ </​tabbox>​
  
  
equations/pauli_equation.txt · Last modified: 2018/04/16 09:09 by jakobadmin