About Me
I completed my undergraduate and master's studies in Natural Sciences (Chemistry) at the University of Cambridge. During my master's research, I worked with Prof. Stuart Althorpe on refining quantum instanton theory on calculating quantum reaction rates.
I will begin my PhD in Chemistry at Caltech in September 2026, where I will continue exploring theoretical and computational approaches to understanding quantum phenomena in chemical systems.
Contact Me
You can email me at ywu10@caltech.edu.
Notes on Path Integrals
- An introduction on various Path Integrals (Incomplete)
- A brief introduction on quantum dynamical methods based on path integrals, namely Ring Polymer Molecular Dynamics and Matsubara Dynamics (Incomplete)
Cambridge Notes
Here are the notes I took when I was at Cambridge. These notes are type-setted using LaTeX, and you can find the source codes on my GitHub. Please let me know if you find any errors.Natural Sciences Tripos, Mathematics
- Part IB Mathematical Methods
Natural Sciences Tripos, Chemistry
Due to departmental regulations, I'm no longer able to provide the chemistry notes unless they are free of the contents created by the lecturers. I'm currently working on this to ensure all the notes published here are (almost) completely original.
The list is here as a placeholder, with the links temporarily removed. I will work on harder to produce more high-quality original notes and put them here as soon as possible.
- Part II A3: High Resolution Molecular Spectroscopy
- Part II A4: Theoretical Techniques
- Part II B7: Statistical Mechanics
- Part II B8: Symmetry
- Part II B10: Electronic Structure
- Part II C6: Diffraction Methods in Chemistry
- Part II C7: Further Quantum Mechanics, with a revision of the systems you learned in Part IB.
- Part II C8: Computer Simulation Methods
- Part II C10: Surfaces and Interfaces (Incomplete)
- Part III M1: Inorganic Materials (Incomplete)
Mathematical Tripos
Obviously I am not majoring in mathematics, so I keep these notes here for reference only. I would recommend Dexter Chua's notes for more comprehensive coverage. I don't revise them frequently, so they contain typos/errors almost surely.
- Part IB Analysis and Topology
- Part IB Complex Analysis
- Part IB Groups, Rings and Modules
- Part II Principles of Quantum Mechanics
Quantum Dynamics
Here are some codes I've produced; the links point to GitHub. None of them are original. They are attempts to replicate the results from the literature and are heavily inspired by my supervisor, Prof. Stuart Althorpe.- RPMD correlation functions: this aims to replicate the results from I. Craig and D. Manolopoulos (2004). It estimates the (Kubo transformed) correlation function for potentials with different degrees anharmonicities.
- RPMD reaction rates: this aims to replicate the results from I. Craig and D. Manolopoulos (2005). It calculates the quantum scattering rates over symmetric and asymmetric 1D Eckart barriers using RPMD.
- Quantum Instanton rates: this again calculates the quantum scattering rate over symmetric and asymmetric 1D Eckart barriers, but using the Quantum Instanton (QI) approach instead. Key references include W. Miller et al (2003), T. Yamamoto and W. Miller (2004) and S. Yang et al (2006), but the sampling methods here are completely different.
- Locating Instanton: this script generalises the saddle-point searching algorithm of Cerjan and Miller (1981) slightly so it can now target saddle points of arbitrary index. This makes it suitable to locate instantons, as illustrated for an asymmetric 1D Eckart barrier in this script.
Electronic Structures
- RHF: this is a code in which I build the closed-shell RHF from scratch. It is for educational purpose only, so it only illustrates the concept, and it is stupidly slow.