Old Man wrote:
"Bjoern Feuerbacher" wrote in message
...

Old Man wrote:

"Andr? Michaud" wrote in message
e.com...


[snip]



To my knowledge, what is being taught, in perfect accordance with
Heisenber's teachings is that the electron is not localized until
the wave function collapses. So, when in motion, it is definitely
considered in the Copenhagen school view of QM as being spread out.


Stationary states aren't subject to uncertainty.

Wrong. Why do you think so???


In what way does Bjoern think that the quantum numbers
of energy, total angular momentum, and parity that together
uniquely define an atomic stationary state carry intrinsic
uncertainty ?

That *some* parameters of stationary states are *not*
uncertain does in no way imply that "stationary states aren't
subject to uncertainty"!!!


The
parameters of an electron in a stationary state can be
measured with precision.

Only the energy can (in principle) be measured with precision in
stationary states. Both position and momentum are "uncertain".


The quantum numbers of energy, total angular momentum,
and parity together uniquely define a stationary state and are
not subject to inherent uncertainty.

Right. But you were not talking merely about these quantum numbers.
You said simply:
"Stationary states aren't subject to uncertainty."
And that's wrong, plain and simple.


Via multiple observations
of identically prepared systems, one can measure the
distribution of degenerate states, that is, states of equal
energy and angular momentum, to unlimited accuracy.

It's not clear to me what you mean by "measure the distribution of
degenerate states".

Additionally, AFAIK, "degenerate states" means only that the energies
are equal. The states can have different angular momenta. E.g. the
states |200 and |210 of the hydrogen atom (using a notation |nlm for
the states here) are degenerate, although the l is different.


The states mentioned are degenerate only in the sense
that the spin orbit interaction has been neglected. Taken
into account, only states of differing z-components of
total angular momentum, J_z, are degenerate in energy.

Right. But that doesn't change the original argument that
"degenerate" means only "have the same energy", not also "have the
same angular momentum".


Even if they are "accidentally" degenerate in energy, a
superposition of atomic stationary states cannot include
states of differing total angular momentum, J, because
they are orthogonal.

So what??? There is no problem with forming a superposition
of mutually orthogonal states! E.g. the spinors (1,0)
and (0,1) (spin in +z or -z direction) are also orthogonal - but
nevertheless the electron can have a spinor 1/sqrt(2) (1,1)
(spin in +x direction), which is obviously a superposition
of (1,0) and (0,1).

And what about the hybrid orbitals of carbon?


Without an external force, a transition
between them is impossible.

A transition between p and s orbitals is impossible???
Ever heard of the selection rule that the angular momentum
has to change by 1 in dipole radiation???


The wave functions don't overlap.

Yes, that's clear. But why on earth should that rule out
a transition between them?


This is also true for Bjoern's example wherein J = L. The
transition, |200 = |210 is impossible without the
application of an external force.

Ever heard of spontaneous emission? The same selection rule
applies here than for stimulated emission.


The electron can't exist in both orbitals at once. They're orthogonal.

The first sentence does in no way follow from the second.


Bye,
Bjoern