Franz Heymann wrote:
"Andrew Usher" wrote in message
om...

This message is a continuation of the discussion in the thread
'Neutrino mass'.

I admit to not being formally educated in QM. I am nevertheless

trying

to criticise a belief normally taught in such education. Although I
don't understand the math involved in the conventional approach, I
believe that I can understand the basics in terms of logic.

The false idea is that the Bohr-Sommerfeld orbits are an incorrect

and

obsolete model of the atom.


The idea that the Bohr-Sommerfeld orbits are an incorrect and an
obsolete model of the atom is in fact quite correct. That approach
led to a dead end and was entirely superceded by quantum mechanics
about seventy years ago.

As we know, the idea of fixed orbits is

not exactly correct, but that does not make it useless.


It is in fact a completely useless and misleading idea.


The orbitals are conventionally given as time-independent
wavefunctions, and that is held to be the correct description.


There is no such thing as a time-independent wave function. A wave is
by defnition a function of space and time. The only reason why the
orbitals are written as time-independent functions is because each of
them has an additional implied factor
exp(iEt/hbar), where E is the energy. So the orbitals are actually
standing waves.


This
leads to the false belief that an electron's position is smeared out
over the orbital,


The probability density for finding the electron at a given position
*is* in fact determined by the orbital.


and that the probability function is independent of
earlier observations.


Those two lines carry no meaning that I can unambiguously discern.


From the uncertainty principle (which states
that particles occupy h^3 in phase space), this can only be strictly
true for the 1s orbital.


Unless you are trying to be clever by making a statement about the
fact that excited states are not stable, I can't follow what you are
driving at.


For all higher n, the relative uncertainty
becomes smaller,


The uncertainty relation relating momentum and position errors is
independent of the quantum number.


and the classical orbit becomes an increasingly
better approximation.

This explains the solar system, for example, where the quantum

numbers

are very, very large and thus quantum effects are unobservable. The
solar system obeys the same physical laws as the atom. There is one
important difference, though: the electrons interact with each other
to such an extent that their orbits would be chaotic even with the
pure Bohr-Sommerfeld orbits.


Right.
Unless they all have the same direction
magnetic field at the same time.
The electrons must all lie in concentric,
co-rotating rings for them not to
interfere with each other yet still
exert over the volume:
http://www.petcom.com/%7Ejohn/H.GIF
http://www.petcom.com/%7Ejohn/He.GIF
http://www.petcom.com/%7Ejohn/Li.GIF
http://www.petcom.com/%7Ejohn/Be.GIF
John