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Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
The cyclic format of the undergraduate physics curriculum depends on students' ability to recall and utilize material covered in prior courses in order to reliably build on that knowledge in later courses. However, there is evidence to…
I explain a direct approach to differentiation and integration. Instead of relying on the general notions of real numbers, limits and continuity, we treat functions as the primary objects of our theory, and view differentiation as division…
Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied…
Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving.…
Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our prior work has shown that…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such…
Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical…
Categorical Quantum Mechanics, and graphical calculi in particular, has proven to be an intuitive and powerful way to reason about quantum computing. This work continues the exploration of graphical calculi, inside and outside of the…
We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical…
Fundamental physics today is best defined operationally: it is the program of identifying the microscopic degrees of freedom, symmetries, and dynamical laws that (i) reproduce the Standard Model (SM) of particle physics, General Relativity…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
This paper provides an approach to establishing the calculus method from the concept of mean, i.e., average. This approach is from a statistics perspective and can help calculus learners understand calculus ideas and analyze a function…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…