I'm essentially a math student working on algorithms for a chemistry problem involving rotational spectra, and I keep coming across references to Wang transformations but have been unable to track down what the Wang basis is. You can assume I have the analysis background to understand what a basis of a function space is.

It was developed by S. C. Wang, as referenced by King, Hainer and Cross in Journal of Chemical Physics 11, pg 27 and S. C. Wang in Physical Review 34, p.243, 1929 (where I think it's defined) It doesn't show up in any of the math texts I have (up to Rudin's Functional Analysis) or any of the classical mech or quantum texts I have (which are more the undergrad level).

Best I can make out is that it transforms the wave functions from a symmetric rotor basis to something that is characterized by representations of the Klien Four group. It's used because it eases the computation of the eigenvalues of the Hamiltonians, used to compute transitions of the rotational spectrum.

So, in short, what is the Wang basis?

  • 2
    $\begingroup$ All the references I can find relate to finance and I ... find my...self...falling asl... $\endgroup$ Jul 25 '12 at 11:49
  • $\begingroup$ @HenryGomersall At least we've got the question in the right neighborhood then ;) $\endgroup$
    – jonsca
    Jul 25 '12 at 13:42
  • $\begingroup$ it's used because it eases the computation of the eigenvalues of the Hamiltonians, used to compute transitions of the rotational spectrum. $\endgroup$ Jul 25 '12 at 16:33
  • $\begingroup$ Okay. The first page of Google results was only coming up with links to a time series technique used in financial data, which was why I assumed it was a standard mathematical transform like the Fourier or Hilbert, so I'm wondering if we're dealing with two separate concepts here. I figured you'd get a specialist answer on this site. Did you look at the Physical Review paper itself, perhaps we need to think of this more as a Physics problem? $\endgroup$
    – jonsca
    Jul 25 '12 at 16:44
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    $\begingroup$ I'd recommend editing the original question with the added details; it would make it easier to locate the info in question. $\endgroup$
    – Jason R
    Jul 26 '12 at 5:00

I don't have enough privileges to comment yet, but you can find the original paper of what later came to be called the 'Wang Transform' here: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

Simply click on the pdf icon under Cached, you'll get a prompt for downloading an apparently broken document, called something like download;jsessionid=AB4D9EB3C11BCA7269B430931924512F.

After saving it, just rename it to whatever you want, with the .pdf extension.

The paper is called 'A class of distortion operators for pricing financial and insurance risks' authored by Shaun S. Wang, originally published in the The Journal of Risk and Insurance, 2000, Vol. 67, No. 1, 15-36.

You may also want a 2nd paper from http://citeseerx.ist.psu.edu/viewdoc/summary?doi= (you'll need to rename the file again).

This paper is called 'A universal framework for pricing financial and insurance risks', by the same author, published in the ASTIN Bulletin, 2002, Vol. 32, 213-234


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