equations:pauli_equation

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equations:pauli_equation [2017/10/21 15:29] jakobadmin created |
equations:pauli_equation [2018/04/16 09:09] (current) 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.1508592561.txt.gz · Last modified: 2017/12/04 08:01 (external edit)

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