advanced_notions:poisson_bracket
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advanced_notions:poisson_bracket [2018/05/05 14:04] jakobadmin ↷ Links adapted because of a move operation |
advanced_notions:poisson_bracket [2018/12/18 14:00] (current) jakobadmin |
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| This is one way to make the difference between quantum and classical mechanics explicit: | This is one way to make the difference between quantum and classical mechanics explicit: | ||
| - | $$ \text{Commutator}\quad [\hat{f},\hat{g}] \quad\longleftrightarrow\quad\text{Poisson bracket}\quad \{f,g\}$$ | + | $$ \text{Commutator}\quad [\hat{f},\hat{g}] \quad\longleftrightarrow\quad\text{Poisson bracket}\quad \{f,g\}$$ |
| ---- | ---- | ||
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| \end{align} | \end{align} | ||
| - | which is extremely similar to the [[equations:canonical_commutation_relations|canonical commutation relations]] in quantum mechanics: | + | which is extremely similar to the [[formulas:canonical_commutation_relations|canonical commutation relations]] in quantum mechanics: |
| \begin{align} | \begin{align} | ||
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| - | Poisson brackets play more or less the same role in [[theories:classical_mechanics:newtonian|classical mechanics]] that [[equations:canonical_commutation_relations|commutators]] do in [[theories:quantum_mechanics:canonical|quantum mechanics]]. | + | Poisson brackets play more or less the same role in [[theories:classical_mechanics:newtonian|classical mechanics]] that [[formulas:canonical_commutation_relations|commutators]] do in [[theories:quantum_mechanics:canonical|quantum mechanics]]. |
| Poisson brackets are also important in thermodynamics, see https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/ and M. J. Peterson, Analogy between thermodynamics and mechanics, American Journal of Physics 47 (1979), 488–490. | Poisson brackets are also important in thermodynamics, see https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/ and M. J. Peterson, Analogy between thermodynamics and mechanics, American Journal of Physics 47 (1979), 488–490. | ||
advanced_notions/poisson_bracket.1525521846.txt.gz · Last modified: 2018/05/05 12:04 (external edit)
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