Subject: CCL: orbitals and reality

From: Alan Shusterman <alan.shusterman=at=reed.edu>
Date: Tue, 01 Feb 2005 00:09:58 -0800

I find the introduction of the trajectory analogy interesting, but I 
think it is inappropriate to equate trajectories with orbitals (maybe I 
misunderstood the analogy?).

I would use trajectories this way:
1. let a classical trajectory be analogous to a complete wave function 
(not an orbital)
2. and suppose we have a complicated system so that the trajectory (like 
a complete wave function) cannot be expressed analytically
3. in this case, we will try to model the trajectory with a combination 
of simpler analytical functions, like short line segments
4. the line segments are analogous to orbitals

Now we can return to the question of what can be measured. We might 
claim that a measurement teaches us something about the trajectory. 
However, it seems misguided to claim a measurement tells us the length 
or direction of the line segments. We only invented the line segments as 
a tool for approximating the trajectory.

Granted, it's not a perfect analogy. But consider one more thing: as we 
approach the limiting situation of an infinite number of infinitely 
short line segments, our trajectory model does approach the actual 
trajectory. On the other hand, the limiting situation of an infinite 
number of orbitals only approaches the Hartree-Fock limit (a model) and 
never the actual wave function. It seems very strange to say we have 
measured orbitals.

-Alan

-- 
Alan Shusterman
Chemistry Department
Reed College
Portland, OR 97202-8199
503-517-7699
http://academic.reed.edu/chemistry/alan/
"The Way you can go isn't the real Way." Lao Tzu