Wolfram Computation Meets Knowledge

Wolfram Summer School


Tyson Jones

Science and Technology

Class of 2017


Tyson Jones studied his bachelor of science at Monash University, Australia, majoring in physics, mathematics and computational science. He’s fascinated by the intersection of physics and computing, recently completing his honors thesis in simulating quantum turbulence and soon starting a PhD in quantum computing at the University of Oxford. Tyson’s research interests include gravitational waves, atomic physics, high throughput computing and quantum information theory. He also holds a love for software architecture and algorithmic design and integrating technology and education.

Computational Essay

Quantum Mechanics »

Project: Analyzing Quantum Systems with(out) Machine Learning

Goal of the project:

To develop simple interfaces for complex quantum mechanical computations and tools for teaching quantum physics, and to explore the prediction of stationary states of arbitrary potentials via machine learning.

Summary of work:

Developed PlotFunctions, EigenFunctions and SimulationFunctions packages for plotting wavefunctions, finding stationary states of arbitrary potentials and simulating wavefunction time-evolution, all via minimal code. The above plots were effectively generated with ShowEvolution[ e–(x–2)2–(y–1)2, Potential → x2+y2] and PlotWavefunction
[e–(1 + i) x2 H1[x], Potential → x2].

Airy functions emerge as eigenstates of triangular potentials through ShowSpectrum[x + 104 UnitStep[–x]]. Invested great effort in making these functions memory and time efficient, supportive of discrete (list) and continuous (pure or interpolating functions and symbolic expressions) inputs, customizable and of elegant architecture. Machine learning training data was prepared by generating random analytic potentials as carefully weighted combinations of polynomials and step functions.

Results and future work:

Spectra of arbitrary potentials, like harmonic, infinite-well and Morse, are very quickly and precisely found. Simulations of interference, coherent behavior, scattering and tunneling can be performed in single-function calls, encoding only a potential and an initial state. Little variation between the ground states of erratic potentials left low-mode prediction as an uninteresting problem for machine learning.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022