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In article <3l0s12FvspcnU2@xxxxxxxxxxxxxx>,
Robert Low <mtx014@xxxxxxxxxxxxxx> wrote:
> Ross A. Finlayson wrote:
> > Robert Low wrote:
> >
> >>Randy Poe wrote:
> >>
> >>>>Keith A. Lewis wrote:
> >>>>
> >>>>>2. No continuum has been discovered in physics -- everything seems to
> >>>>>change in finite units called quanta. That's the real world.
> >>>
> >>>Perhaps someone has pointed this out, but the energy
> >>>levels of unbound particles are a continuum. It is
> >>>only binding forces that give rise to discrete states.
> >>
> >>Sufficiently high energy states of an electron
> >>in a Hydrogen atom also have a continuous energy spectrum.
> >>
> >>See
> >>
> >>http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
> >>
> >>for example.
> >>
> >>
> >>>In general, I am not sure. I don't even know if we
> >>>have a closed-form solution for any atom more complex than
> >>>hydrogen.
> >>
> >>Heck, we don't even have a closed-form solution for
> >>the classical three-body problem. And in fact, we
> >>know that there isn't one.
> >
> > I'll disagree with that.
>
> That's probably because you don't understand the
> statement. There is no analytic function into
> which you can feed the initial positions and
> velocities of three bodies interacting via
> Newtonian gravitation and from which you can
> subsequently compute their position at arbitrary
> times.
>
> Of course, there are numerical and approximation
> schemes that allow you to work these quantities
> out to any precision you care about.
There are also, of course, some initial conditions for which analytic
solutions exist, but they are sparse in the phase space of all possible
initial conditions.
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