Research-based interactive simulations to support quantum mechanics - - PowerPoint PPT Presentation

Research-based interactive simulations to support quantum mechanics learning and teaching

Antje Kohnle University of St Andrews

GIREP-MPTL 2014 International Conference, 7-12 July, Palermo

www.st-andrews.ac.uk/physics/quvis quantumphysics.iop.org

The QuVis team

• Development of simulations and accompanying activites:

Antje Kohnle

• Students coding simulations: Martynas Prokopas, Aleksejs

Fomins, Joe Llama, Inna Bozhinova, Gytis Kulaitis + others

• Final year project students: Bruce Torrance, Anna Campbell,

Scott Ruby, Cory Benfield + others

• Technical support: Tom Edwards, Alastair Gillies
• Faculty involved in evaluation: Christopher Hooley, Charles

Baily, Natalia Korolkova, Donatella Cassettari, Bruce Sinclair, Georg Hähner, Friedrich Koenig, Noah Finkelstein, Catherine Crouch, Gina Passante + others

• Eur. J. Phys. 31 (2010) 1441-1455; Am. J. Phys. 80 (2012) 148-153

Outline

• Challenges of quantum mechanics instruction
• Interactive simulations
• Overview of the QuVis resources
• Development process and evaluation outcomes
• Conclusions and future plans

Challenges of quantum mechanics instruction

“I will never believe that god

plays dice with the universe.”

– Albert Einstein “I think I can safely say

that nobody understands quantum mechanics.”

– Richard Feynman “Learning quantum mechanics is challenging.” – Chandralekah Singh, University of Pittsburgh

• Counterintuitive

behaviour which disagrees with our classical intuition.

• Phenomena that can not

be observed directly.

(c) 1989 Hitachi Ltd.

• Complicated mathematics

required to solve even simple phenomena.

• Instruction often focuses on

simplified abstract models.

Observing screen Double slit Electron source Observing screen

Challenges of quantum mechanics instruction

Outline

• Challenges of quantum mechanics instruction
• Interactive simulations
• Overview of the QuVis resources
• Development process and evaluation outcomes
• Conclusions and future plans

Resources shown recommended in the 2014 MPTL review Review process: E Debowska et al., Eur. J. Phys. 34 (2013) L47 www.um.es/fem/PersonalWiki/pmwiki.php/MPTL/Evaluations

Making the invisible visible

S B McKagan et al, AJP, 76, 406 (2008) http://phet.colorado.edu/

Zhu and Singh, Phys Rev ST PER 8, 010118 (2012) http://www.compadre.org/psrc/items/detail.cfm?ID=6814 Belloni and Christian, Am J Phys, 76, 385 (2008)

position x probability density ψ x

2

Visualizing complicated time-dependent behaviour to help build physical intuition

Challenging students’ classical ideas by allowing them to assess whether they can explain experimental outcomes

The potential of interactive simulations

• Engage students to explore

physics topics through interactivity (student agency), prompt feedback (trial and error exploration) and multiple representations.

• Through careful interaction

design, implicitly guide students towards the learning goals.

• Activities promote guided

exploration and sense-making.

e.g. Podolefsky et al., Phys Rev ST PER, 6, 020117 (2010)

Interactivity and student agency

Simulation/activity Group 2 (N=48): Group 1 (N=34): Screenshots/activity

not enjoyable very enjoyable Group 1: 20/29 comments similar to “Much easier to play around with simulations so that you can run tests and experiments.”

13/14 St Andrews level 2 Quantum Physics

10 20 30 40 50

1 2 3 4 5

Percent of students

1 hour workshop session, Hidden Variable simulation

Outline

• Challenges of quantum mechanics instruction
• Interactive simulations
• Overview of the QuVis resources
• Development process and evaluation outcomes
• Conclusions and future plans

QuVis: www.st-andrews.ac.uk/physics/quvis

17 simulations 50 simulations 18 simulations NEW: sims for touchscreens research-based; freely available for use

• nline or download;

introductory to advanced level

QuVis: www.st-andrews.ac.uk/physics/quvis

problem sets, password- protected solutions available to instructors

QuVis: www.st-andrews.ac.uk/physics/quvis

One collection embedded in a full curriculum at quantumphysics.iop.org developing introductory quantum theory using two-level systems

IOP quantum physics: quantumphysics.iop.org

Kohnle et al., Eur J Phys, 35, 015001 (2014)

Derek Raine (Leicester) Project lead and editor Pieter Kok (Sheffield) Author Quantum information Mark Everitt (Loughborough) Author Foundations

• f qm

Dan Browne (UCL) Author Quantum information Antje Kohnle (St Andrews) Simulations Physics education Elizabeth Swinbank (York) Editor; Physics education

IOP quantum physics: quantumphysics.iop.org

Christina Walker (IOP) Project manager

2 4 6 8 10 12 14 16 18 20

Bohr atom Copenhagen Separation of variables Series solution Variational method t-indep pert Fermi rule Dirac equn Identical particles 2nd quantisation Photon statistics Radiative trans Entanglement Bell Qubits Quantum crypt. Spin

core

• ptions

neither

Quantum mechanics curricula in the UK

Survey by Derek Raine (Leicester), 2011

Birmingham Bristol Cambridge Exeter Galway Glasgow Heriot-Watt Hertfordshire Hull Imperial Kent King's Leicester Loughborough Sheffield St Andrews Strathclyde Sussex Swansea UCL Warwick York

IOP resources: novel material for these and other topics suitable for a first university course in quantum physics

Number of institutions

Advantages of developing introductory quantum theory using two level systems (spin ½ particle, two-level atom, single photons in an interferometer):

• Focus on experiments that have no classical explanation.
• Focus on interpretive aspects of quantum mechanics.
• Focus on quantum information theory (two-level systems

are qubits).

• Mathematically less challenging: basic algebra versus

differential equations and calculus. Some linear algebra included in the IOP resources.

IOP quantum physics: quantumphysics.iop.org

Michelini, Ragazzon, Santi and Stefanel (2000), Scarani (2010), Malgieri, Onorato & De Ambrosis (GIREP 2014)

In-class trials: level two Quantum Physics (Scottish level two = first year university elsewhere)

• The photoelectric effect; single photon experiments.
• Spin; successive Stern-Gerlach experiments; entanglement;

hidden variables

• Matter waves; the Schrödinger equation; energy eigenstates;

infinite and finite square wells

Pre-lecture readings from the IOP Quantum Physics resource Workshop: Interferometer experiments simulation Homework: Phase shifter in a Mach-Zehnder interferometer Workshop: The expectation value of an operator Workshop: Entangled spin ½ particle pairs versus hidden variables Homework: Quantum cryptography

PART 1 PART 2

Two-level systems at the introductory level

9/18 lectures

• n two-level

systems 2014 (N=73): 2013 (N=68): 5/16 lectures

• n two-level

systems

level 2 Quantum Physics

10 20 30 40 50 60

1: much less difficult 2 3 4 5: much more difficult Percent of students 2013 2014

Perceived difficulty of Quantum Physics part 1 (two-level systems) compared with part 2 (wave mechanics)

Two-level systems at the introductory level

2013 (N=70) 2014 (N=87) Significant differences with large effect sizes.

Two-level systems Wave mechanics p-value for paired t-test Effect size Exam 2013 (Instructor A)

71.7% 56.7% p<0.005 0.82

Exam 2014 (Instructor B)

83.8% 68.5% p<0.005 0.61

Effect size =

difference in means average standard deviation

Outline

• Challenges of quantum mechanics instruction
• Interactive simulations
• Overview of the QuVis resources
• Development process and evaluation outcomes
• Conclusions and future plans

“How useful for learning quantum physics have you found the simulations used in the course?”

5 10 15 20 25 30

13/14 level two Quantum Physics (N=73) 5 simulations 13/14 level three Quantum Mechanics (N=57) 17 simulations

5 10 15 20 25 30 35

Student perceptions

“I wish for the simulations to remain in Advanced Quantum Mechanics.”

13/14 level four Advanced Quantum Mechanics (N=16) 4 simulations

2 4 6 8 10 12

Evaluation and refinement using student feedback key in developing educationally effective resources.

Student perceptions

Developing educationally effective simulations

considers research on

• student

difficulties

• interaction

design

• visualization

Initial design

• physics

student coders

• iterative

revisions during coding

Coding

• revisions to

all simulations and activities wherever appropriate

Observation

sessions

• revisions
• ideas for new

simulations

In-class trials

student difficulties: Johnston et al (1998), Bao & Redish (2002), Wittmann et al (2005), Singh (2008) , ... interaction design: Clark & Mayer (2008), Adams et al (2008), Podolefsky et al (2010), Saffer (2010), ... visual representations: Adams et al (2008), Lopez and Pinto (2014), Chen and Gladding (2014), ...

Individual student

• bservation sessions

Free exploration (implicit scaffolding) Work on activity (difficulties, revisions) Investigating visualizations

In-class trials

Surveys (student perceptions) Observations (interface design) Analytics of control use (interface design) Activity responses (difficulties) Pre- and post-tests (learning gains) Comparative studies (effectiveness)

Research methods

New Quantum curriculum collection (17 simulations)

• 42 hours of observation sessions (17 sims, 19 students)
• in-class trials in using 9 simulations

Kohnle et al., 2013 PERC Proceedings

At the heart of quantum mechanics lies the superposition principle:

physics.stackexchange.com

Visualizing non-classical states

For a single photon in an interferometer: 1 2 |top path > + 1 2 |bottom path >

• Example: Visualizing the photon superposition state
• Aim: facilitate the development of a productive mental model

for introductory-level students

importance of mental models: Baily & Finkelstein, Phys Rev ST PER (2010)

Visualizing non-classical states

• 2013 in-class trials at St Andrews and US institution: V1 led some

students to develop incorrect ideas about quantum superposition.

• Animations for four revised visualizations of photon superposition
• Student interviews (N=9): students describe what the visualizations

suggest to them and choose from a list of 13 statements. Original (V1) (V2) (V3) (V4, adopted) (V5)

Visualizing non-classical states

Limitations:

• Small region of “parameter

space” explored

• Small number of interviews

(N=9) Revised (V4) adopted

2 4 6 8 V2 V3 V4 V5 Number of students

productive: Phase relationship between the two paths is maintained

1 2 3 4 5 V2 V3 V4 V5 Number of students

incorrect: Photon splits into two half-energy photons

Results from in-class trials

Limitations: 2013 only use of simulation, 2014 additional reading and lecture on single photon interference “What happens when a photon encounters a beamsplitter?” Interferometer simulation, St Andrews level two, coded responses

10 20 30 40 50 60 70

Percent of students

V1, 2013 (N=28) V4, 2014 (N=76)

takes

• ne path

detection reveals path takes both paths splits into two photons

• ther

V1 V4

inter-rater reliability: Cohen's Kappa 0.62-1 𝜓2 4, 𝑂 = 104 = 15.9, exact 𝑞 = 0.003

making sense of the visualizations

“Ah yes, so, umh, again these two are

• connected. One is

slightly brighter than the other suggesting that the probability of them arriving at detector 1 is greater than at detector 2. That does seem to be the case as they pass through – there seems to be a bit more in detector 1 than in detector 2.”

Observation sessions

making predictions and testing them experimentally

Observation sessions

[moves phase shift to 2π] “I guess this will go back to detector 1 as you would suspect. And again with 4π.” [moves phase shift to 4π]”

generalizing results to come up with general rules

Observation sessions

[moves to 3π] “... an odd number

• f π produces a

wave going directly to detector 2, an even number produces a photon heading directly to detector 1 and then in between sort of the probability slowly gradually shifts from detector 1 to detector 2.”

Observation sessions

[points to expectation value panel] “The expectation value – I’m not really sure what that is. It’s got a kind of hat on it. Is there something I missed in the introduction?”

Observation sessions

Is there anything in the simulation you can find to help you understand the expectation value better? Would the following additional control / information .... help you? Would the following rephrasing of the text / activity help you? ... Using this, can you derive / explain the formula for the expectation value shown? aim: find patterns in student difficulties and ways to overcome them.

• Hilbert space; Matrix formalism of QM; Pure and

mixed states via the density matrix.

• Entanglement; reduced density matrix; entropy of

entanglement

• Quantum teleportation; quantum cryptography – the

BB84 protocol

• Quantum computing

Homework (review): Graphical representation of complex eigenvectors Homework: Superposition states and mixed states Homework: Entanglement: the nature of quantum correlations Homework: Quantum key distribution

In-class trials: Advanced Quantum Mechanics (Scottish level four = third year university elsewhere)

Do students achieve the learning goals?

assess success in completing challenges

0% 20% 40% 60% 80% 100%

unanswered incorrect partially correct correct

? is mixture 20/80 mixture ?? is super- position, correct coefficients N=20, level 4 Advanced QM

Superposition states and mixed states: success in completing challenges

Pre- and post-test question (abbreviated) An equal mixture of | ↑> and | ↓> and particles each in a superposition 1/ 2(| ↑> + ↓> are experimentally indistinguishable. Particles in a superposition are actually in state | ↑> and | ↓> , we just don’t know which. Particles in a superposition state actually oscillate rapidly in time between | ↑> and | ↓> . If we measure a different component of spin than Sz, we can experimentally distinguish between the two. Simulation/activity Pre-test Post-test

1 week

Does the simulation enhance student learning?

20 40 60 80 correct partially correct incorrect Percentage of students

no certainty rating uncertain somewhat uncertain somewhat certain certain

20 40 60 80 correct partially correct incorrect

N=20, level 4 Advanced QM

Pre-test Post-test

Superposition states and mixed states: pre- and post-test outcomes

Simulation activities

1) Have a play with the simulation for a few minutes, getting to understand the controls and displays. Note down five things about the controls and displayed quantities that you have found out. Question 1 correct (N=52) Question 1 not answered (N=13) p-value for t-test (two-tailed) Correct activity problems (excludes Q1) 5.2 4.1 0.01

Cryptography simulation, level 2, 2014

Question 1 may be important for success on the activity. Question 1 for all simulation activities:

Driving questions may optimize exploration: Adams et al., PERC Proceedings, 2009

Outline

• Challenges of quantum mechanics instruction
• Interactive simulations
• Overview of the QuVis resources
• Development process and evaluation outcomes
• Conclusions and future plans

Conclusions

• Research-based interactive simulations can address

challenges of quantum mechanics instruction (and other topics) through student agency, implicit guidance, trial and error exploration and multiple representations.

• An iterative development process informed by student

feedback from individual sessions and in-class trials is key to developing educationally effective resources.

• Initial evidence that QuVis simulations are helping students

learn quantum mechanics topics, including topics such as entanglement and hidden variables at the introductory level.

Future plans

• Extend the QuVis HTML5 collection to include amongst
• ther topics more simulations on quantum information

processing and single photon experiments; for the school and university level; revise old simulations.

• Include more game-like elements aligned with learning

goals.

• More open and exploratory activities, including intrinsically

collaborative activities.

• Multi-institution evaluation studies and more community

input into development. Volunteers welcome! Contact: Antje Kohnle, ak81@st-andrews.ac.uk