Re: Cubic Complex Variables / Applications
- From: "Symmetry Observer" <mathexpert@xxxxxxxxxxxxx>
- Date: 10 Dec 2005 13:28:40 -0800
N:dlzc D:aol T:com (dlzc) wrote:
> Dear Symmetry Observer:
>
> "Symmetry Observer" <mathexpert@xxxxxxxxxxxxx> wrote in message
> news:1134068209.267959.179170@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >
> > N:dlzc D:aol T:com (dlzc) wrote:
> >> Dear Symmetry Observer:
> >>
> >> "Symmetry Observer" <mathexpert@xxxxxxxxxxxxx> wrote in
> >> message
> >> news:1133412017.131873.263980@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >> ...
> >>The electron
> >> orbitals overlap, so an "instantaneous" transition
> >> between said orbitals is no big thing either.
> >>
> > Yes but the average area enclosed by different
> > orbitals are most likely different.
>
> Yes, but the electron can "express" along a changed orbital
> without having to be in a different position to do it. Except as
> a starting point.
>
Ok let's discuss the orbitals of the Bohr atom but first we should
review the basics of classical kinematics that are associated with
uniform acceleration.
We have
x = (1/2)*a*t^2
(eq.1)
where x = x(t) is displacement as a function of t,
a denotes the uniform acceleration and t is the time.
Differentiating with respect to time
dx/dt = v = at
(eq.2)
where v denotes velocity. We may write
t = v/a
(eq.3)
Substituting (eq.3) into (eq.1) results in
x = (1/2)*a*(v/a)^2
x = (1/2)*v^2/a
(eq.4)
Solving (eq.4) for a gives us
a = (1/2)*v^2/x
(eq.5)
Now let's see if we can identify some constants of
nature that correspond with x and v and that are
also connected with optical phenomena and/or the
hydrogen atom. What about writing the following
v = c and x = a_o,
where c is the speed of light
and a_o is the Bohr radius? If we substitute these
into (eq.5) then the resulting value of a becomes
a candidate for L the "start - up" acceleration of
photons. We may therefore write (as a preliminary
approximation) for L the "start up" acceleration
of photons
L = (1/2)*c^2/a_o
(eq.6)
A quick calculation will show that L is indeed
sufficiently large to be considered as a candidate
for the universal acceleration limit.
.
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