The October issue of the American Journal of Physics featured the research of Janine Shertzer, professor of physics, and Sean McAlinden ’15, physics major, not only within its pages, but also on its cover. Their paper, titled “Quantum scattering from cylindrical barriers,” was published in the monthly, peer-reviewed, scientific journal, with one of the paper’s figures included as the leading image of the issue.
Neither Shertzer nor McAlinden expected that what started out as a summer research project would result in publication in the American Journal of Physics. After completing the summer research project — aimed to solve a simple one-dimensional quantum scattering problem using the finite element method, and to compare the result with the analytical solution — McAlinden refused to stop.
The pair decided to move on to tackling the scattering problem in two-dimensions, which led to 11 months of developing a sophisticated finite element code to solve the Schrodinger equation for a cylindrical potential.
“When I searched the literature, I was surprised to find that no one had solved the Schrodinger equation numerically in cylindrical coordinates,” explains Shertzer. “We decided to write a paper and submit it to the American Journal of Physics. We were thrilled when the paper was accepted and one of our figures was chosen for the cover of the October 2016 issue.”
Beyond the success of this research, Shertzer makes note of the substantial role McAlinden played in the actual research process.
“Sean was not my undergraduate research assistant; Sean was my collaborator,” says Shertzer. “He motivated this project and made significant contributions every step of the way.”
Shertzer describes the published paper in further detail below:
“We gain important information about the quantum world through scattering. If you send a beam of particles into a region with some known potential, you can predict the angular distribution of the scattered particles by solving the Schrodinger equation.
“Experimentalists can measure this angular distribution in the laboratory with an array of particle detectors. The Schrodinger equation can be solved analytically for only a few simple potentials. Numerical solutions are also difficult because the scattering boundary conditions involve the unknown angular distribution. In this paper, we use the finite element method to solve the Schrodinger equation in cylindrical coordinates.”
Read the paper on the American Journal of Physics website.
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