Gerald Davenport

School: Richard J. Daley College

Major: Electrical Engineering

DOI: https://doi.org/10.21985/n2-98dt-8v14

Biography:

Gerald is a second year student at Richard J. Daley Community College focusing on engineering. He is interested in control systems, robotics and mechatronics. Gerald is currently conducting research in Noncommutative Quantum Calculus. He plans to pursue a career in Electrical Engineering. Gerald is a member of MESA | Mathematics, Engineering, Science, Achievement, IEEE Student and the Engineering Club at Richard J. Daley. In his spare time, Gerald enjoys listening and dancing to music.

Noncommutative Quantum Calculus

One of the central problems in modern physics is the issue of reconciling the microscopic description of nature (given by Quantum mechanics) with the macroscopic (classical physics). From the mathematical point of view, variables in classical physics commute with each other (meaning ab=ba), but in the quantum world, variables are not commutative (ab≠ba). There were many different attempts to develop a quantum version of mathematics that can include both classical and quantum physics throughout the years. Being that calculus is the main mathematical tool in classical physics, in our work, we develop a noncommutative version of classical calculus. This is very similar to regular calculus (and include classical calculus as a special case), but variables do not commute with each other. We will present basic definitions and examples of noncommutative derivatives, antiderivatives, integrals, and differential equations.

References:

[1] Kac, V., Cheung, P.. ( 2002) Quantum Calculus, Springer. New York

Author Q&A

What is your research topic, in a nutshell?

The development of a noncommutative version of classical calculus.

How did you come to your research topic?

My interest in doing research in mathematics lead me to the collaboration with Dr. Oseledets, who suggested the topic of “Quantum noncommutative Calculus”.

Where do you see the future direction of this work leading (how might future researchers build on your work or what is left to discover in this field)?

Creating a mathematically defined bridge between the microscopic description of nature given by Quantum Mechanics and the macroscopic.

Where are you heading to after graduation?

An electrical engineering program but presently I have not been accepted yet.