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small typo fix in the tutorial
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positr0nium committed Nov 18, 2024
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Expand Up @@ -58,7 +58,7 @@ For **Bosons** the ladder operators obey `commutator <https://en.wikipedia.org/w
For **Fermions** the ladder operators obey anti-commutator laws:

.. math::
\{a_i, a^\dagger_j\} = a_i a^\dagger_j + a_j a^\dagger_i = \delta_{ij}\\
\{a_i, a^\dagger_j\} = a_i a^\dagger_j + a_j^\dagger a_i = \delta_{ij}\\
\{a^\dagger_i, a^\dagger_j\} = \{a_i, a_j\} = 0
Note that the fermionic laws imply $a_i^\dagger a_i^\dagger = 0$. This means that an operator, which tries to insert two particles in the same state will immidiately become 0 and therefore not contribute. This is known as `Pauli exclusion principle <https://en.wikipedia.org/wiki/Pauli_exclusion_principle>`_.
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