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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?

jonsca
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Michael Conlen
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    All the references I can find relate to finance and I ... find my...self...falling asl... – Henry Gomersall Jul 25 '12 at 11:49
  • @HenryGomersall At least we've got the question in the right neighborhood then ;) – jonsca Jul 25 '12 at 13:42
  • it's used because it eases the computation of the eigenvalues of the Hamiltonians, used to compute transitions of the rotational spectrum. – Michael Conlen Jul 25 '12 at 16:33
  • 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? – jonsca Jul 25 '12 at 16:44
  • I think it is a transform in the sense of a Fourier transform to a basis in terms of sine and cosine, but it's not the financial one (that Wang published in 2000). I think the early papers are in physics journals since J. chem phys didn't exist then. I've been digging through the Wang paper and another by Van Vleck (phys rev. 33, 467), but I'm way out of my league with those.

    I had assumed that this was something someone in computational spectroscopy would be readily familiar with, and had hoped one of those people might be a member here on stack exchange.

     – Michael Conlen Jul 25 '12 at 16:57
  • No worries, this isn't time critical; thanks for looking out. – Michael Conlen Jul 25 '12 at 19:22
  • It's physical review without the letter, if you're on their site it's near the bottom of the drop down, second from bottom.

    http://prola.aps.org/

     – Michael Conlen Jul 26 '12 at 00:41
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    I'd recommend editing the original question with the added details; it would make it easier to locate the info in question. – Jason R Jul 26 '12 at 05:00

1 Answers1

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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=10.1.1.197.337

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=10.1.1.112.5957 (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