theories:quantum_mechanics:phase_space
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theories:quantum_mechanics:phase_space [2018/05/04 16:12] jakobadmin [Intuitive] |
theories:quantum_mechanics:phase_space [2018/05/05 12:40] jakobadmin ↷ Links adapted because of a move operation |
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| this density can take provocative negative values and, indeed, these can | this density can take provocative negative values and, indeed, these can | ||
| be reconstructed from lab measurements [11]. | be reconstructed from lab measurements [11]. | ||
| + | <cite>[[https://arxiv.org/abs/1104.5269|Quantum Mechanics in Phase space]] by Curtright and Zachos</cite> | ||
| </blockquote> | </blockquote> | ||
| Line 70: | Line 70: | ||
| where $\{\{ ,\}\}$ denotes the Moyal bracket and $\{ ,\}$ the [[advanced_notions:poisson_bracket|Poisson bracke]]t. | where $\{\{ ,\}\}$ denotes the Moyal bracket and $\{ ,\}$ the [[advanced_notions:poisson_bracket|Poisson bracke]]t. | ||
| - | In the limit, $\hbar \to 0$ the von Neumann equation reduces to the [[basic_tools:phase_space:liouvilles_theorem|Liouville equation]]. | + | In the limit, $\hbar \to 0$ the von Neumann equation reduces to the [[theorems:liouvilles_theorem|Liouville equation]]. |
| The difference between the von Neumann equation and the Liouville equation is that in the former the density of points in phase space is not conserved. Formulated differently, the probability fluid is diffusive and compressible. | The difference between the von Neumann equation and the Liouville equation is that in the former the density of points in phase space is not conserved. Formulated differently, the probability fluid is diffusive and compressible. | ||
theories/quantum_mechanics/phase_space.txt · Last modified: 2018/10/11 15:02 by jakobadmin
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