UCSD PHYS 142/242: Computational Physics — Stochastic Methods and Path Integrals (Fall 2026)

UCSD PHYS 142/242: Computational Physics — Stochastic Methods and Path Integrals (Fall 2026)#

Author: Javier Duarte

The registrar lists this course under its catalog title, “Computational Physics II: PDE and Matrix Models,” which predates how the course is now taught. The description below is what the course actually covers.

Course information#

This course is an upper-division undergraduate course and introductory graduate course on computational physics, focusing on stochastic methods: Monte Carlo integration, Markov chain Monte Carlo, and the statistical analysis of simulation output. We develop these methods in the setting of Feynman’s path integral formulation of quantum mechanics, which turns quantum mechanical problems into high-dimensional integrals that are natural targets for sampling. The course will explore both the theoretical foundations and computer implementations. Students will develop their own code to solve the physics applications. Basic knowledge of calculus, quantum mechanics, Linux, and programming in some language is expected.

The course structure will consist of weekly lectures on conceptual topics, e.g., quantum mechanics and Monte Carlo theory, and lab sections on computational tools, e.g., programming in Python and C/C++. Students will learn how to apply physical reasoning to programming, optimize and debug code, create simulations of physical systems, and report results with honest uncertainties. Students will also learn how to use modern tools to efficiently solve scientific computing problems: interpreted (Python) vs. compiled (C/C++) languages and how to link the two. There will be 3 individual homework assignments, 4 short in-class quizzes, and 3 individual oral checkpoints. There will also be a final project in which students will work in groups. AI tools are permitted on homework and projects, provided their use is disclosed; see the syllabus for the full policy.

PHYS 141/241 and PHYS 142/242 are independent companion courses covering deterministic and stochastic methods, respectively. Neither is a prerequisite for the other, and they may be taken in either order.

Student learning outcomes#

Upon successful completion of Physics 142/242, students will be able to:

Design computer programs to numerically solve physics problems, like the harmonic oscillator using the Feynman path integral approach.
Estimate and report statistical uncertainties on Monte Carlo results, accounting for autocorrelation between samples.
Validate a stochastic calculation against an independent deterministic one (e.g., matrix diagonalization) and explain any residual discrepancy quantitatively.
Consider multiple approaches and compare their computational performance, accuracy, and fidelity to physical laws.
Find and choose the best tool or programming language for the task.
Use AI coding assistants effectively and critically: verify generated numerical code against physical and statistical benchmarks, and recognize its characteristic failure modes.
Visualize the solutions.
Collaborate with peers to tackle complex, realistic problems.
Present findings, and defend the technical choices behind them.