By Andrew Lee

Biswaroop Mukherjee â09 achieved a mathematical simulation that has never been done before, according to physics teacher Antonio Nassar. Mukherjee carried out a simulation of a wave-packet tunneling through a rectangular barrier using a computational software program called Mathematica.

“Since a quantum particle is expressed as a wave, it interferes with itself, creating all sorts of interesting patterns in time,” Mukherjee said.

This simulation was done previously in other programming languages, including Basic, Fortran, C++, but never in Mathematica, Nassar said.

Mathematica is a computer program used for scientific engineering and other mathematical fields.

Mukherjee posted a movie on YouTube about his research project, which displays the probability distribution of the particle as a function of position.

Mukherjee did this simulation as an extension of his work at a summer internship.

He started out by finding a program that solves the SchrÃ¶dinger equation and learning quantum mechanics. He then found a C++ program, translated it into Mathematica and altered the parameters. His research project had erroneous results before it finally worked.

Mukherjee was able to finish his project for his Studies in Scientific Research class in December.

“It would have been very difficult without the Studies in Scientific Research [class],” Mukherjee said.

He plans on advancing his research project in several more phases this year.

“Iâll try adapting the schroedinger equation to fit an extended electron, that is, a charged particle that has a noticeable radius,” he said.

Mukherjee arrives to school early frequently to work on his research in the Math Lab, Nassar said. Mukherjee plans on posting his project on the Wolfram research site.