Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
individual
Campus
Daytona Beach
Authors' Class Standing
Yaohua Zhao, Sophomore
Lead Presenter's Name
Yaohua Zhao
Lead Presenter's College
DB College of Engineering
Faculty Mentor Name
Dr. Keshav Acharya
Abstract
We discuss Feynman’s method of differentiating with respect to a parameter inside an integral and explore its significance on selective topics of modern physics. This powerful technique allows us to integrate functions that may seem impossible. Depending on the underlying parameters, the Feynman method becomes a unifying framework that connects mathematical concepts to many parameter-dependent equations in modern physics. In statistical mechanics, this appears directly in the partition function, where derivatives with respect to temperature-related parameters yield thermodynamic quantities such as internal energy and heat capacity; this demonstrates how parameter dependence gives rise to macroscopic behaviors observable at a larger scale. In quantum mechanics, similar techniques provide insight into how systems respond to changes in potential or external conditions.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Analysis Commons, Quantum Physics Commons, Statistical, Nonlinear, and Soft Matter Physics Commons
Differentiating the Impossible: Feynman's Trick in Applications of Modern Physics
We discuss Feynman’s method of differentiating with respect to a parameter inside an integral and explore its significance on selective topics of modern physics. This powerful technique allows us to integrate functions that may seem impossible. Depending on the underlying parameters, the Feynman method becomes a unifying framework that connects mathematical concepts to many parameter-dependent equations in modern physics. In statistical mechanics, this appears directly in the partition function, where derivatives with respect to temperature-related parameters yield thermodynamic quantities such as internal energy and heat capacity; this demonstrates how parameter dependence gives rise to macroscopic behaviors observable at a larger scale. In quantum mechanics, similar techniques provide insight into how systems respond to changes in potential or external conditions.