Evaluation of inverse integral transforms for undergraduate physics students

Authors: Farrell, Aaron; van Zyl, Brandon P.; MacDonald, Zachary

Source: Canadian Journal of Physics, Volume 90, Number 1, January 2012 , pp. 1-9(9)

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Abstract:

We provide a simple approach to the analytical evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind our method is to reduce the inverse transform to the solution of an ordinary differential equation. We illustrate the utility of our approach by providing examples of the evaluation of transforms without the use of tables. We also demonstrate how the method may be used to obtain a general representation of a function in the form of a series involving the Dirac delta distribution and its derivatives, which has applications in quantum mechanics, semiclassical, and nuclear physics.

Keywords: 02.30.Uu; 02.30.Zz; 01.40.gb; 02.30.Uu; 02.30.Zz; 01.40.gb

Document Type: Research article

DOI: http://dx.doi.org/10.1139/p11-135

Publication date: 2012-01-12

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Published since 1929, this monthly journal reports significant advances in research in physics, including atomic and molecular physics, condensed matter, elementary particles and nuclear physics, gases, fluid dynamics and plasmas, electromagnetism and optics, mathematical physics, and interdisciplinary, classical, and applied physics. It publishes research articles, rapid communications, and review articles contributed by recognized experts in Canada and abroad. It also publishes special issues dedicated to current research in a particular area of physics.
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