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Are there any established theories for non-holonomic quantum mechanics? I have googled for d'Alembert's principle, non-holonomic constraints and quantum mechanics but only found an abstract talking about golden nanocars so would like to know if there had been any progress.

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  • $\begingroup$ Interesting question, but it's not clear to me what would even be meant by nonholonomic quantum mechanics. What would it even mean, quantum-mechanically, to constrain an electron's velocity without constraining its position? If we constrain its velocity, then doesn't its uncertainty in position become infinite by the uncertainty principle? $\endgroup$
    – user4552
    Jan 16, 2018 at 21:56
  • $\begingroup$ Ben: perhaps it can be constrained probabilistically or something? Hope someone has insight. $\endgroup$
    – Emil
    Jan 16, 2018 at 22:31
  • $\begingroup$ The whole point of setting forth Hamiltonians at a classical level is to get rid of constraints and fictitious forces which pop-up in the Newtonian approach. I cannot see the relevance of this in quantization. $\endgroup$
    – DanielC
    Jan 16, 2018 at 22:50
  • $\begingroup$ As I understand it Hamiltonians cannot describe physics with nonholonomic constraints, so it should be relevant? $\endgroup$
    – Emil
    Jan 16, 2018 at 22:55
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    $\begingroup$ I might be answering to the void here, but I just ran into this thread and wanted to pass along a reference to an article I co-wrote with a chemist on precisely this topic (quantum nonholonomic mechanics): nature.com/articles/s41598-018-33023-8. $\endgroup$ Oct 26, 2022 at 1:16

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