equations:pauli_equation
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equations:pauli_equation [2018/03/13 11:14] jakobadmin |
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> |
| - | <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, | ||
| - | * $\phi$ 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. $ | ||
| - | <-- | ||
| - | </note> | ||
| - | <tabbox Why is it interesting?> | + | <tabbox Intuitive> |
| - | The Pauli equation is the correct non-relativistic equation to describe spin $1/2$ particles. | + | The Pauli equation describes how the state of a quantum system with [[basic_notions:spin|half-integer spin]] changes in time. |
| - | <tabbox Layman> | + | In contrast, the [[equations:schroedinger_equation|Schrödinger equation]] describes the time evolution of systems without spin. |
| - | + | <tabbox Concrete> | |
| - | <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]]. | 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.1520936053.txt.gz · Last modified: 2018/03/13 10:14 (external edit)
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