Learn Quantum Mechanics with Haskell

TL;DR

This paper proposes an educational approach for quantum mechanics that integrates laboratory experiments with mathematical formalism using Haskell, enhancing intuition and computational skills for students.

Contribution

It introduces a dual-language learning method combining laboratory simulations and mathematical calculations in Haskell to improve understanding of quantum mechanics.

Findings

Students gain intuition through laboratory language simulations.

Students can perform complex quantum calculations in Haskell.

The method bridges theory and experiment effectively.

Abstract

To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The laboratory ideas are naturally expressed in one language, and the theoretical ideas in another. We present a method for learning quantum mechanics that begins with a laboratory language for the description and simulation of simple but essential laboratory experiments, so that students can gain some intuition about the phenomena that a theory of quantum mechanics needs to explain. Then, in parallel with the introduction of the mathematical framework on which quantum mechanics is based, we introduce a calculational language for describing important mathematical objects and operations, allowing students to do calculations in quantum mechanics, including calculations that cannot be done by hand. Finally, we ask students to use the calculational language to implement a simplified version of the laboratory language, bringing together the theoretical and laboratory ideas.