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I Smallest possible orbit and velocity of a particle?

  1. May 25, 2017 #1
    If the units of angular momentum are quantised in integer amounts of ##\hbar##, does that then imply that we have restrictions on the smallest possible radius ##r## of an orbit of a given mass ##m##, given that the speed of light is ##c##. As follows,

    $$\hbar=m\bf{r}\times \bf{v}$$, where v is the velocity of the particle of mass m, if the velocity vector and radius are perpendicular then we have,


    and if we account for relativity, we have


    If we now take the minimum radius to be the plank length l, we have for the maximum velocity of a particle with the minimum orbital angular momentum


    Which always gives v<c, which makes sense but I'm not sure if this result is correct?
  2. jcsd
  3. May 25, 2017 #2


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    Relativity and quantum mechanics are not fully compatible, so one can expect to run into problems when one tries to do a calculation involving both for very very small, close objects.

    I think once the distance between an 'orbiting' and an 'orbited' object becomes small enough, one would have to analyse it using pure quantum mechanics, not a mixture of that and relativity. The QM derivation of the orbitals of a hydrogen atom is an example of that.
  4. May 25, 2017 #3


    Staff: Mentor

    It's not meaningful because quantum objects don't have classical orbits.
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