Subject: Anharmonicity

From: Herbert Homeier t4720 <[email-masked]>
Date: Mon, 25 Nov 96 12:17:01 +0100

Please excuse if you receive this message twice.

"Jens Spanget-Larsen" <[email-masked]> wrote:
---------------------------
CCL:

On Friday, 15 Nov 1996, I posted the following question: 

> In a study of molecular vibrational structure I have encountered a 
> normal mode with a "symmetrical" anharmonic potential V of the form: 
> 
> V(Q) = a*Q^2 + b*Q^4
> 
> i.e., the potential V as a function of the normal coordinate Q can be 
> approximated by a fourth order polynomial in Q, containing only the 
> second and the fourth power. What are the solutions to the 
> vibrational eigenvalue problem with this potential function? I would 
> be most grateful for information on literature that deals with this 
> problem.

I immediately received a number of useful replies, that are 
summarized below. Thank you to all that replied!

Yours, Jens >--<
 
(summary omitted)
-------------------------- 

It may be of interest that there are a number of results of Weniger and
Meissner regarding this type of anharmonic oscillator that are online
available via our server at
 
http://www.chemie.uni-regensburg.de/preprint.html

These are based on perturbation theory (Weniger. Beware: the usual
perturbation series as sketched in one of the responses in the summary
is strongly divergent. This, however, does not mean that it is useless.
The problems can be handled.) and the generalized Bloch equation that
can be solved iteratively (Meissner). 

There is also a poster of Meissner at ECCC3 ---accessible via
http://hackberry.chem.niu.edu:8000
http://www.chemie.uni-regensburg.de:8000 (mirror) --- 
that summarizes some of his results.
--------------------------------------------------------------
Dr. Herbert H. H. Homeier
Institut fuer Physikalische und Theoretische Chemie
Universitaet Regensburg, D-93040 Regensburg, Germany
Phone: +49-941-943 4720  FAX: +49-941-943 4719/+49-941-943 2305
email: [email-masked]
WWW: http://rchs1.uni-regensburg.de/~c5008
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