Subject: Re: CCL:Orbitals

From: elewars <elewars{at}trentu.ca>
Date: Thu, 29 May 2003 10:18:15 -0400

2003 May 29

Hello,

So you are saying that there is a one-to-one correspondence between physically real things X and
QM operators X^ , the average value of the thing X for a system being the integral of the system's
wavefunction over the operator. So orbitals are real only if there is, mathematically, an orbital
operator PSI^--which there is not (?). Good point.

EL
======

Leif Laaksonen wrote:

> Hi,
>
> I might remember wrong from my primary courses in quantum chemistry
> that only obsrvables are the expectation values from the wave
> function!
>
> This means that while the wave function (|P>) as such is not
> observable the expectation value of property X is (<P|X|P>).
>
> Regards,
>
> -leif
>
> -----Original Message-----
> From: Computational Chemistry List [mailto:chemistry-request{at}ccl.net] On Behalf Of Guosheng Wu
> Sent: Wednesday, May 28, 2003 7:46 PM
> To: chemistry{at}ccl.net
> Subject: CCL:Orbitals
>
> > > > --- elewars <elewars{at}trentu.ca> wrote:
> > > > > 2003 May 28
> > > > >
> > > > > Are MOs physically real? This is a meaningful question only if there is some
> > > > > experiment or observation that could provide an answer _yes_ or _no_.  Is there,
> > > > > at least in principle, such an experiment or observation?
>
> > > Guosheng Wu wrote:
> > >
> > > > MO is just a useful mathematical tool for quantum chemistry/physics, and
> > > > it seems to me itself does not have much physical meaning.
> > > >
> > > > However, many properties from MOs are meaningful and can be observed
> > > > by exmperiments: such as the square of absolute MOs (|MO|^2) corresponding
> > > > to the electronic density. Things like |MO|^2 of d-orbitals were published
> > > > in a Science article last one or a few years.
>
> > --- elewars <elewars{at}trentu.ca> wrote:
> > > Hello,
> > >
> > > Thanks for your ideas. If photoel. spectra (and Koopmans theorem--in this case the
> > > second MO is at the ionization limit) really measure the energy difference of two MOs,
> > > then MOs exist!
> > >
> > > In any case, it is an interesting discussion.
> > >
> > > EL
> > > =====
>
> The properties from |MO|^2 exist does not really mean MO exists.
>
> When we know some properties from x^2 exist and can be measured,
> this does not mean x exists and can be measured.
>
> For example, what does the complex number(i) mean in the real world?
> Measurable? Not really, but obviously it's a useful mathematical tool
> for lots of applications. Certainly (i^2=-1) means something. Right?
>
> Related issue for absolute energy: energy difference is measurable
> by many kind of experiments, but not for the absolute energy.
>
> This may lead to some kind of philosophical problem, if one has
> such a taste.
>
> Guosheng
>
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