Dimensional Perturbation Theory on the Web!

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A complete resource center for the study of dimensional perturbation theory (DPT).

For now, a list of references in Prof. Deborah Watson's bio will get you started.  Professor Watson is head of the dimensional perturbation theory group in the Department of Physics at the University of Oklahoma.

I have made some of these references downloadable.

John Walkup, et al.

On the behavior of Pade approximants in the vicinity of avoided crossings. Although not strictly related to DPT, this Journal of Chemical Physics article uses the Barbanis potential to study the relationship between avoided crossings and the convergence of Pade approximants, important for summing the perturbation series resulting from DPT. M. Dunn, D.K. Watson, and J.R. Walkup J. Chem. Phys., 104 , 9870, (1996).
Dimensional expansions for atomic systems. This chapter, authored by D.K. Watson, M. Dunn, T.C. Germann, D.R. Herschbach, D.Z. Goodson, and J.R. Walkup, is from the book New Methods in Quantum Theory, edited by C.A. Tsipis, V.S. Popov, D.R. Herschbach, and J. Avery, NATO Conference Book, Vol. 8 (Kluwer Academic, Dordrecht, Holland, 1996).
Avoided crossings of diamagnetic hydrogen as functions of magnetic field strength and angular momentum. This article focuses on the relationship between the locations of avoided crossings in two important spectra of diamagnetic hydrogen. J.R. Walkup, M. Dunn, and D.K. Watson, Phys. Rev. A, 58, 4668-4682, (1998).
Branch-point structure and the energy characterization of avoided crossings. This is the companion paper to "Avoided Crossings of diamagnetic hydrogen..." (see above), and analytically establishes the mathematical arguments used in the previous paper. J.R. Walkup, M. Dunn, and D.K. Watson, J. of Math. Phys., 41, 218-239, (2000).
Local optimization of the summation of divergent power series.* We recently developed a new technique for summing divergent and poorly-convergent power series. In the following paper we tested this method on the power series of known functions, and introduce a physical application from our research on diamagnetic hydrogen. J.R. Walkup, M. Dunn, and D.K. Watson, J. Math. Phys., 41, 5814-5831 (2000).
Energy Calculations of Low |m| diamagnetic hydrogen states with dimensional perturbation theory. In this brief report, we show that DPT can sum the energy levels of diamagnetic hydrogen at low values of |m|, even |m|=0. The optimization technique detailed in the paper above is used as well. J.R. Walkup, M. Dunn, and D.K. Watson, accepted for publication by Physical Review A.
Here is the poster we presented in Washington DC this year at the DAMOP conference.

John Carzoli, et al.

Bret McKinney, et al.

Improved large N limit for Bose-Einstein condensates from perturbation theory. Presents a perturbation solution for a model Bose-Einstein Hamiltonian derived by Bohm, Esry, and Geene, using 1/N as the perturbation parameter, where N is the number of particles in the condensate. D.K. Watson and B.A. McKinney, Phys. Rev. A, 59, 4091 (1999).
Semiclassical perturbation theory for two electrons in a D-dimension quantum dot. B.A. McKinney and D.K. Watson, To appear in Phys. Rev. B, 61 (2000).

Martin Dunn, et al.

Continuation of the Schroedinger Equation for Higher Angular Momentum States to D Dimensions and Interdimensional Degeneracies. M. Dunn and D.K. Watson
Continuation of the Wave Function for Higher Angular Momentum States to D Dimensions. II. Elimination of Linear Dependencies. M. Dunn and D.K. Watson

Students (Current and Former) of Dimensional Perturbation Theory

John Walkup is working on understanding the relationship between avoided crossings and the branch point sctructure of diamagnetic hydrogen. You can also check out his Curriculum Vita and his personal interests. He has now made the energy coefficients of diamagnetic hydrogen calculated with dimensional perturbation theory available online. (Ph.D., April, 2000)

John Carzoli is applying DPT to excited states of helium.  (Ph.D., Spring, 2001)

Brett McKinney is now applying DPT to special topics in Bose-Einstein condensation. He has his own personal web page  (Ph.D., expected Summer, 2001)

Collaborators and Other Researchers

Martin Dunn, Deborah Watson's fomer post-doctoral researcher, still lives in Norman and is still highly active in all phases of DPT research.

Tim Germann has been heavily involved with our group in the study of dimensional perturbation theory. On his web page he has a list of his publications, many of which are downloadable.

Another researcher heavily involved in DPT is David Goodson. An extensive list of publications, with downloadable abstracts, is provided.

Alexei Sergeev has published many important papers on DPT. A list is available on his website, also with downloadable abstracts. Hopefully, we can provide them right here in the future.

John Loeser at Oregon State University has also done much research in this area.

Vladimir Popov has been involved in DPT right from the very start.

Send any questions to John Walkup