Subject: Re: CCL:[Re]: orbitals and reality

From: Lou Noodleman <lou_at_scripps.edu>
Date: Mon, 24 Jan 2005 14:33:17 -0800 (PST)

To CCL group:
I want to add a short addition to my previous post, in response
to some comments within the discussion.
(1) In the discussion, someone proposed that orbitals cannot
represent reality when the orbital is complex.
This notion contradicts the basic principles of quantum mechanics,
since both electron densities and currents, representing the flow
of electron density, are represented by wavefunctions-for one
electron, these are orbitals. It is readily shown from the
conservation of probability that the equation for a current
takes a particular form. Only complex wavefunctions (that is,
those with both a real + an imaginary part) have a nonzero
current. Thus, complex wavefunctions are often required,
whenever there is a current. (See for example, Merzbacher (1970)
pp.35-39 (Chapter 4); an extensive discussion is found in D. Bohm,
Chapter 4 (1951)). Eqivalently, one can use two coupled real
functions.
(2) Someone also proposed that "empty" orbitals were absurd,
since properties cannot depend on "empty" orbitals.
However, "empty" or "virtual orbitals" are the simplest example
of final states, and the transition from an initial ("occupied")
state to a "final" ("empty" or unoccupied) state is fundamental
within quantum mechanics. The probability for the transition
> from i to f is a function of both i and f, P(i->f)= |A (i->f)|
squared, where A is a matrix element depending on both i and f.
Neither of these ideas are absurd or contradictory, and do not
conflict with reality either for "orbitals" or more generally
for wavefunctions.
Lou Noodleman
The Scripps Research Institute
.
.