Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
theories:classical_mechanics:koopman_von_neumann_mechanics [2018/05/03 13:04] jakobadmin ↷ Links adapted because of a move operation |
theories:classical_mechanics:koopman_von_neumann_mechanics [2018/12/18 12:54] jakobadmin |
||
---|---|---|---|
Line 5: | Line 5: | ||
<tabbox Intuitive> | <tabbox Intuitive> | ||
- | Koopman-von-Neumann Mechanics is a reformulation of [[theories:newtonian_mechanics|classical mechanics]] using the same language that we usually only use in [[theories:quantum_mechanics:canonical_quantum_mechanics|quantum mechanics]]. | + | Koopman-von-Neumann Mechanics is a reformulation of [[theories:classical_mechanics:newtonian|classical mechanics]] using the same language that we usually only use in [[theories:quantum_mechanics:canonical|quantum mechanics]]. |
Usually in classical mechanics, our main focus is the trajectories of objects. | Usually in classical mechanics, our main focus is the trajectories of objects. | ||
Line 16: | Line 16: | ||
The equation of motion in Koopmann-von-Neumann mechanics is a complexified reformulation of the classical Liouville equation (which handles probability distributions over the phase space). | The equation of motion in Koopmann-von-Neumann mechanics is a complexified reformulation of the classical Liouville equation (which handles probability distributions over the phase space). | ||
- | * See the notes by Frank Wilczek on [[http://frankwilczek.com/2015/koopmanVonNeumann02.pdf|"Koopman von Neumann Mechanics, and a Step Beyond"]] | + | * See the notes by Frank Wilczek on [[https://web.archive.org/web/20170206103038/http://frankwilczek.com/2015/koopmanVonNeumann02.pdf|"Koopman von Neumann Mechanics, and a Step Beyond"]] |
* See also this [[https://physics.stackexchange.com/a/80822|nice answer at StackExchange]] | * See also this [[https://physics.stackexchange.com/a/80822|nice answer at StackExchange]] | ||
* [[https://arxiv.org/pdf/quant-ph/0301172.pdf|Topics in Koopman-von Neumann Theory]] -a Ph.D. Thesis by Danilo Mauro | * [[https://arxiv.org/pdf/quant-ph/0301172.pdf|Topics in Koopman-von Neumann Theory]] -a Ph.D. Thesis by Danilo Mauro |