✎ Phase Space Quantum Mechanics [The Physics Travel Guide]

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====== Phase Space Quantum Mechanics ======

<tabbox Intuitive> 
<blockquote>Classical statistical mechanics is a ' crypto-deterministic'
theory, where each element of the probability distribution of the dynamical
variables specifying a given system evolves with time according to deterministic
laws of motion; the whole uncertainty is contained in the form of the initial distributions.
A theory based on such concepts could not give a satisfactory account of such
non-deterministic effects as radioactive decay or spontaneous emission (cf. Whittaker
(2)). Classical statistical mechanics is, however, only a special case in the general
theory of dynamical statistical (stochastic) processes. In the general case, there is
the possibility of 'diffusion' of the probability 'fluid', so that the transformation with
time of the probability distribution need not be deterministic in the classical sense.
In this paper, we shall attempt to interpret quantum mechanics as a form of such
a general statistical dynamics.

<cite>[[https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9D0DC7453AD14DB641CF8D477B3C72A2/S0305004100000487a.pdf/quantum_mechanics_as_a_statistical_theory.pdf|Quantum Mechanics as a statistical theory]] by J. E. Moyal</cite>
</blockquote>

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**Reading Recommendations**

* [[https://arxiv.org/abs/1104.5269|Quantum Mechanics in Phase space]] by Curtright and Zachos
  
<tabbox Concrete> 
**Reading Recommendations**

* 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
  * [[https://arxiv.org/abs/1104.5269|A Concise Treatise on Quantum Mechanics in Phase Space]] by Thomas L. Curtright, David B. Fairlie, & Cosmas K. Zachos,  World Scientific, 2014.

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**Important Papers**

* [[https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9D0DC7453AD14DB641CF8D477B3C72A2/S0305004100000487a.pdf/quantum_mechanics_as_a_statistical_theory.pdf|Quantum Mechanics as a statistical theory]] by J. E. Moyal
<tabbox Abstract>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

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