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path integral

In 1983, Pres. Ferdinand Marcos established a system of national centers of excellence in the basic sciences. The first institutes to be created were the National Institute of Physics (NIP), the National Institute of Geological Sciences (NIGS), and the Natural Science Research Institute (NSRI) at the University of the Philippines (UP) in Diliman and the Institute of Mathematical Sciences (IMS, now the Institute of Mathematical Sciences and Physics, IMSP), the Institute of Chemistry (IC), and the Institute of Biological Sciences (IBS) at the UP’s Los Baños campus.

In this series of blog posts, I will trace the history of the UP Diliman institutes from the perspective of published research. This post in particular, highlights the most exciting research paper from these institutes in the first decade (1983-1993). In my next post, I will give you a historical sketch of the National Institute of Physics during this decade with the help of  Dr. Chris Bernido, NIP’s first Director.

There were few papers published during this time.  There were only 20 research articles – 17 from the National Institute of Physics, 3 from the Natural Science Research Institute and none from the National Institute of Geological Sciences. I have listed all the papers from this decade here.

Most papers in Physics are from the theoretical Physicists (authors: C. Bernido, M.V. Carpio-Bernido, J. Magpantay, D.M. Yanga); the experimental papers are mostly in optics and signal processing (authors: C. Saloma, V.R. Daria). The NSRI papers are on plant cell tissues (author: S.C. Halos). More on this on my next post.

The most exciting research paper that came out during this decade is a mathematical physics paper by M.V. Carpio-Bernido. The author uses path integration to solve interesting noncentral potentials exactly.

Solutions to noncentral potentials are important in quantum physics and chemistry. For example, the Hartmann potential as well as the Quesne potential are used to model ring-shaped molecules such as benzene. The solutions could also be used in scattering problems that involve nonspherical scatterers.

As new more complex materials are synthesized, or as scattering phenomena have gone beyond symmetric scatterers, this research becomes even more relevant.

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Path integral quantization of certain noncentral systems with dynamic symmetries

M.V. Carpio-Bernido, J of Mathematical Physics 32 1799-1807 (1991). DOI: 10.1063/1.529244

Abstract

Path integral quantization is done for the five classes of potentials appearing in the systematic search for nonrelativistic systems with dynamical symmetries done by Makarov, Smorodinsky, Valiev, and Winternitz [Nuovo Cimento A 52, 1061 (1967)]. By an iterated application of Bateman’s series formula to the polar coordinate path integral, an expansion is obtained on the Feynman kernel or the Green’s function, whichever is possible, in terms of hypergeometric functions of the polar and azimuthal parts and a radial path integral is obtained whose evaluation yields the energy eigenvalues and the normalized wave functions. Special cases include the Hartmann potential and the ring-shaped oscillator.

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Addendum

Another paper of M.V. Carpio-Bernido that is also worth mentioning is about the calculation of the Green function for an axially symmetrical potential field via path integral evaluation (J of Phys A-Mathematical and General 24, 3013-3019 (1991).  DOI: 10.1088/0305-4470/24/13/016). Among the paper published during this decade, this paper had the most number of citations. This paper is also one of the NIP’s most cited paper.

The first paper with an address from the new institutes is from D.M. Yanga and J. Magpantay. In this paper, they derived the Lee-Yang term for velocity-dependent potentials using stochastic quantization (Phys Rev D 32, 516-518 (1985). DOI: 10.1103/PhysRevD.32.516).

 

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