equations:pauli_equation
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equations:pauli_equation [2018/03/13 11:12] jakobadmin |
equations:pauli_equation [2018/03/26 16:38] jakobadmin |
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| - | ====== Pauli Equation ====== | + | ====== Pauli Equation: $ \quad \left( \frac{1}{2m}(\vec \sigma ( \vec p - q\vec A))^2 + q\phi \right) \Psi = i \hbar \partial_t \Psi $ ====== |
| - | + | ||
| - | <note tip>$$ \left( \frac{1}{2m}(\vec \sigma ( \vec p - q\vec A))^2 + q\phi \right) \Psi = i \hbar \partial_t \Psi $$ | + | |
| - | -->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?> | <tabbox Why is it interesting?> | ||
| - | The Pauli equation is the correct non-relativistic equation to describe spin $1/2$ particles. | + | The Pauli equation is the correct __non-relativistic__ equation to describe spin $1/2$ particles. |
| <tabbox Layman> | <tabbox Layman> | ||
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| * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond | * Nonrelativistic particles and wave equations by Jean-Marc Lévy-Leblond | ||
| - | --> Common Question 1# | ||
| - | + | <tabbox Definitions> | |
| - | <-- | + | |
| - | --> Common Question 2# | + | * $\Psi$ 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, | |
| - | <tabbox Examples> | + | * $\vec A$ the vector potential, |
| - | + | * $\phi$ the electric scalar potential and | |
| - | --> Example1# | + | * $\hbar$ the reduced Planck constant. |
| - | + | ||
| - | + | ||
| - | <-- | + | |
| - | + | ||
| - | --> Example2:# | + | |
| - | + | ||
| - | + | ||
| - | <-- | + | |
| - | | + | |
| - | <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
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