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> |
| - | + | * Ψ is the wave function, | |
| - | <-- | + | * m the mass of the particle, |
| - | + | * q the charge of the particle, | |
| - | <tabbox History> | + | * →σ the Pauli matrices, |
| + | * →p the momentum, | ||
| + | * →A the vector potential, | ||
| + | * ϕ the electric scalar potential and | ||
| + | * ℏ the reduced Planck constant. | ||
| + | Take note that →σ, a "vector of matrices" is only used as a convenient short-hand notation for the sums that appear in the equation. For example, →σ→p=σ1p1+σ2p2+σ3p3. | ||
| </tabbox> | </tabbox> | ||
equations/pauli_equation.1508592561.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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