Related Experiment Video
Updated: Oct 20, 2025

Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research
Published on: February 16, 2024
Schrödinger principal-component analysis: On the duality between principal-component analysis and the Schrödinger
Ziming Liu1, Sitian Qian2, Yixuan Wang3
1Department of Physics, Massachusetts Institute of Technology, Cambridge Massachusetts 02139, USA.
Abstract:
Principal component analysis (PCA) has been applied to analyze random fields in various scientific disciplines. However, the explainability of PCA remains elusive unless strong domain-specific knowledge is available. This paper provides a theoretical framework that builds a duality between the PCA eigenmodes of a random field and eigenstates of a Schrödinger equation. Based on the duality we propose the Schrödinger PCA algorithm to replace the expensive PCA solver with a more sample-efficient Schrödinger equation solver. We verify the validity of the theory and the effectiveness of the algorithm with numerical experiments.
Related Concept Videos
The Quantum-Mechanical Model of an Atom
The Pauli Exclusion Principle
The Uncertainty Principle
Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates
When a particle moves relative to an inertial frame, the equations of motion can be expressed using rectangular components. If the motion is confined to the x-y plane, the equations having the x and y coordinates only can be used to simplify the mathematical representation.
However, when particles...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
Molecular Orbital Theory I

