Professor Jeongho Kim at the Department of Applied Mathematics has been selected for the Samsung Future Technology Incubation Program to conduct research on numerical methods for two-dimensional quantum models interacting with electromagnetic fields

The Samsung Future Technology Incubation Program aims to advance basic science in Korea and nurture world-class scientists and technologists. This initiative identifies and funds innovative research projects, and Professor Kim plans to use this opportunity to solve quantum equations numerically.

The movements of objects we observe in everyday life can be explained by Newton’s laws of motion. However, these laws fall short in describing the behavior of extremely small particles, such as atoms and electrons. Quantum mechanics has provided a framework to explain the movements of these infinitesimal particles, fueling significant advancements in mathematics, physics, and other basic sciences, as well as diverse engineering fields.

In quantum mechanics, the motion of particles is described by the Schrödinger equation, a mathematical formula. Finding solutions to this equation is essential for predicting particle movements. However, due to the lack of an exact formula, scientists rely on approximations, often utilizing algorithms and computers to find these solutions.

Pioneering numerical methods for quantum models interacting with electromagnetic fields
Over the past few decades, several methodologies have been proposed to solve quantum equations numerically. However, analyzing quantum models that interact with electromagnetic fields remains underexplored, as maintaining physical properties becomes challenging when electromagnetic fields are involved. Professor Kim aims to develop a numerical method for two-dimensional quantum models interacting with electromagnetic fields and to prove its convergence. His goal is to solve the Chern-Simons-Schrödinger and Chern-Simons-Dirac models stably and numerically.

Professor Kim has a background in the theory and numerical methods of fluid equations, and he plans to adapt these methodologies to quantum equations. “We are the first in the world to theoretically explore numerical methods for quantum models interacting with electromagnetic fields. If successful, this research will advance the analysis of numerical methods for interacting electromagnetic fields and provide stable numerical solutions for physics, engineering, and other fields through pre-experimental simulations,” said the professor.

The ultimate aim is to uncover the connections between quantum equations and fluid equations. Professor Kim articulated his vision, saying, “My goal is to explore the relationship between them and establish the corresponding physical theories.”