quantum education, VR, and intuition  

Can you touch a wavefunction?

Audun Skau Hansen

Chief Research Officer @ Myreze
Previously: Senior lecturer @ KURT/UiO/Hylleraas

About me

Education

KURT/UiO, Learning Assistant Program

Quantum

The Hylleraas Centre for Quantum Molecular Sciences

R&D

Myreze, 3D Deep Learning

Active learning:

Students do more than just listen

Emphasis on developing student skills

Higher order thinking

Engagement in activities

Reflection on own learning

Bonwell, C. C., & Eison, J. A. (1991). Active learning: Creating excitement in the classroom. 1991 ASHE-ERIC higher education reports. ERIC Clearinghouse on Higher Education, The George Washington University, One Dupont Circle, Suite 630, Washington, DC 20036-1183.
Active Learning at the Faculty of Mathematics and Natural sciences, UiO:

The Learning Assistant (LA) program at UiO [*]

A pedagogic support unit (KURT)

Centre for Computing in Science Education

B-tjenesten (student tutoring service)

Interactive computational projects (spinoff from the Hylleraas centre for quantum molecular sciences)

[*] Odden, T. O., Lauvland, A., Bøe, M. V., & Henriksen, E. K. (2023). Implementing the Learning Assistant Model in European higher education. European Journal of Physics.

Hylleraas Centre for Theoretical Chemistry

A Centre of Excellence developing simulation methods for molecules in complex and extreme environments.

The Question

 

Textbook orbitals

Interactive VR orbitals

 

Can you touch a wavefunction?

The collection of exactly solvable 1D toy quantum systems is far from infinite!
For computational QM, it's different.

Wavefunctions from Research

Model of the Structure of Penicillin, Dorothy Hodgkin, Oxford

The "Impossible" Course

Physical Chemistry II – Intro to Quantum Chemistry

Course scope

→ Intro QM (Dirac notation, particle-in-a-box, hydrogen)

→ Many-body QM (helium, molecules, ab initio)

→ Time-dependent QM (time evolution, IR, spectroscopy)

10 credits, but basically a full bachelor unpacked.

Cognitive bottlenecks

 

Abstract notation

Hilbert spaces, bra-ket, determinants

Multiple scales

electrons, molecules, chemistry

Weak visual intuition

Static blobs in textbooks

Active learning helps, but...

Even in LA-driven settings, students struggle to grasp wavefunctions, electron correlation,
nodal structures, and quantum mechanical properties like spin and phase.

Can tangible, interactive representations aid learning?

The Quantum Workforce Challenge

Workforce shortage & skill mismatch

Almost all participants agreed that the relevance of Quantum Technologies for industry will increase significantly in the near future (...). This shows the relevance of getting industry workforce ready to work with quantum technologies.

— Greinert et al., PRPER 2023

Workforce shortage & skill mismatch

"With the growing number of startups, companies, universities, large corporations, and government agencies that are accelerating the quantum technologies industry, the problem of skills shortage on both, demand and supply side, cannot be ignored.

— Kaur & Venegas-Gomez, 2022

Education is concentrated at grad/PhD level

"To meet the future need, we believe that aspect needs to change with Quantum Information Science and Technology (QIST) education being incorporated into the curricula at predominantly undergraduate institutions and community colleges in the US"

— Perron et al., QUEST 2021

The gap

Most quantum chemistry & computing practitioners:

masters and PhDs

 

What we also need:

Engineers, technicians, quantum-aware developers

→ Better intuition-building tools

A brief encounter with quantum chemistry

 

 

 

 

The universe is dynamic and has structure
Particles can have wave properties

 

 

 

 

Louis De Broglie's waves (1924)
$(-\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial x^2} + V(x) ) \Psi = i \hbar \frac{\partial}{\partial t}\Psi$

 

Erwin Schrödinger's equation (1925)
Max Born's interpretation (1926)

From one particle to many

Helium: 2 electrons, 1 nucleus

$-\frac{\hbar^2}{2m_e}\left(\nabla_1^2 + \nabla_2^2\right)\Psi - \frac{2e^2}{4\pi\epsilon_0}\left(\frac{1}{r_1} + \frac{1}{r_2}\right)\Psi + \frac{e^2}{4\pi\epsilon_0}\frac{1}{r_{12}}\Psi = E\Psi$

 

The molecular Schrödinger equation
$E(\Psi_t) = \frac{\langle \Psi_t | \hat{H} | \Psi_t \rangle }{\langle \Psi_t | \Psi_t \rangle} \geq E_0$

 

The variational principle

Any trial wavefunction gives energy ≥ exact ground state

Requirements on $\Psi(x_1, x_2)$

 

  • Correct number of electrons
  • Normalizable: $\int |\Psi|^2 dx_1 dx_2 = 1$
  • Antisymmetric: $\Psi(x_1, x_2) = -\Psi(x_2, x_1)$
  • Physically reasonable fragmentation
Slater determinant

Hartree product: $\psi_1(x_1)\psi_2(x_2)$

↓

Slater determinant: $\frac{1}{\sqrt{2}}[\psi_1(x_1)\psi_2(x_2) - \psi_1(x_2)\psi_2(x_1)]$

A basis function

$| \phi \rangle$

A basis set

$\{ | \phi_i \rangle \}$

Local vs delocalized basis functions

Basis expansion

$| \psi \rangle = \sum_i | \phi_i \rangle c_i$

The visualization problem

 

Students see orbitals as

static isosurfaces in a book

 

What if we could walk into the basis expansion?

Stepping Inside

Braketlab as a didactic tool

Computational lab

 

Visualizing electron correlation

Closing the Loop

Can you touch a wavefunction?

 

Probably not literally, but we can provide a

tangible representation

of wavefunctions, where more of their logic is intrinsic.

Practical applications

 

→ Enable more quantum "toy systems"
→ On-ramp for non-physics students into quantum theory
→ Learn by trial and error in a consistent environment

 

Thank you!

audun@myreze.com