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 [2018/10/11 15:02] (current) jakobadmin [Concrete] |
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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> | ||
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| 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. | ||
| Line 80: | Line 80: | ||
| **Reading Recommendations** | **Reading Recommendations** | ||
| + | * A great introduction is [[https://arxiv.org/abs/1602.06071|The algebraic way]] by Hiley | ||
| * See also the corresponding chapter in Ballentine's Quantum Mechanics book, and also | * See also the corresponding chapter in Ballentine's Quantum Mechanics book, and also | ||
| * [[http://aapt.scitation.org/doi/pdf/10.1119/1.16475|Canonical transformation in quantum mechanics]] Y. S. Kim and E. Wigner | * [[http://aapt.scitation.org/doi/pdf/10.1119/1.16475|Canonical transformation in quantum mechanics]] Y. S. Kim and E. Wigner | ||
theories/quantum_mechanics/phase_space.1525443162.txt.gz · Last modified: 2018/05/04 14:12 (external edit)
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