thinking like a physicist: the paradigms curriculum at...

Thinking like a Physicist:The Paradigms Curriculumat Oregon State University

Janet TateDepartment of Physics

Oregon State UniversityPresented at the 2008 March Meeting of theAmerican Physical Society, New Orleans, LA

www.physics.oregonstate.edu/paradigms

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Outline

• Thinking like a physicist• Paradigms/Capstones in Physics

reorganize content, new pedagogy

• Computation• Solid state & nanoscience examples

from the courses• Research projects

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Thinking like a physicist

Physicsknowledge

Capacity forself-, peer-, lay-

instruction

Creativityintuition

independence

Experimentalskill

Mathematical skill

Conceptual skill

Computational skill

Multiplerepresentations

Critical, analyticalthinker

ability to generalize

Consummateproblem-solver

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Multiple Representations

• Algebraic

bn =2

!f x( )sin

n2" x

!dx

0

!

#

A periodic function can be represented asa sum of harmonic sinusoidal functionswhose coefficient is the projection of thatfunction onto the relevant harmonic.The extent to which harmonic is represented in the sumhas profound consequences for the quantum wavefunction, the electrical signal, etc.

• Geometric

• Verbal

• Graphical

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Paradigms & Capstones

SrC

Jr

So

Fr •Intro Ph•Intro ComputationalPhysics

•Modern Ph•Intro Ph•Intro Ph

•Solid State•AMO•Nuclear/particle•Senior thesis

•QuantumMechanics

•Thermal Physics•Optics

•Math methods•E & M

•Energy & Entropy•Periodic Systems•Rigid Bodies /Reference Frames

•Classical mech

•Spin & QuantumMeasurements

•1-D Waves•Central Forces

•Symmetries &Idealizations

•Static VectorFields

•Oscillations

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Characteristics of Paradigms

• Case-study method (small pieces)• Explicit attention to middle-level transition• Active engagement• Span 2 or more subdisciplines• Early Quantum Mechanics• Quantum & Classical base• Collaborative faculty planning (buy-in)

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Active Engagement

• Verbalization teaches clear thinking• De-emphasize teacher-as-oracle• Activate intuition• Active problem solving• Encourage peer-instruction• Efficiency

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Computation in the Paradigms

• OSU offers B.S. in Computational Physics; firstcourse in Maple and Java feeds Paradigms

• Visualization• Calculation• Simulation• Animation• Requires literacy, but not expert coding skills• “Reach for the computer” to solve a problem• D. H. McIntyre, J. Tate, and C. A. Manogue,

Integrating Computational Activities into the Upper-Levelparadigms in Physics Curriculum at Oregon State University,Am. J. Phys. (2008, in press).

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Computation in the Paradigms

• Spins & Quantum Measurement via Stern-Gerlachsimulation

• Projection; superposition; change of basis• Same language as Fourier analysis• “Real” experiment to determine quantum state

Oven z-Analyser x-Analyser z-Analyser result?

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Solid State & Nanoscience

• Spend time on fundamental ideas and ways of thinking;later complexity is more easily understood.

• Early quantum mechanics• Couple to modern ideas

Quantum wellsCarbon nanotubesSemiconductors & defectsSpin valves, GMR

• Motivation to learn more• Opportunity to do research• Attention to professional development

AJP journal paper; 10-minute talk

2-D

periodic intwo directions

3-D

periodic inthree directions

1-D

periodic inone direction

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GaInP/AInP Quantum Well Laser Diode

Quantum Wells to Bands

Relevant, modern examples

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Quantum Wells to Bands

Boundary conditions,eigenstates, and Schrödinger’sequation all have to do withproducing light

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Periodic Square Wells

• Periodic square well develops energy band conceptand defect idea

• Qualitative and quantitative

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Doped Semiconductor (Si:P)

• Learning a differentdialect is useful!

• Explicit instruction

-

Si[Ne] 3s2 3p2 [Ne] 3s2 3p3

+P

Engineer’s pictureChemist’s picture

Eg

Real picture

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Dispersion: waves in a rope

• Easy, familiar, but rich example• Dispersion concept is new• Normal modes, superposition,

boundary conditions,experiment, limits

• Measure normal-mode λ, f

• Measure τ, µ• Plot ω vs. k

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Coupled Oscillators

• Students find period and wavelength from simulation• CUPS DOS-based software (revision in progress)

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Diatomic chain

Dispersion, gaps, modes,boundaries, evanescent waves

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Silicon

EF

[ ]00,,kk =!

!"

#$%

&=

333

kkkk ,,!

Real Bandstructure - Si

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Superposition

• LCAO approach to solids: need molecularorbitals, density of states, and partial density ofstates

• Begins with Fourier analysis in Oscillations• Continues with Stern-Gerlach in Spins• Finite well in Waves & H-atom in Central Forces• Superpositions in Quantum Mechanics

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Bandstructure; DoS computation

• Senior solid state class• Analytical: cubic systems, single-

orbit models in LCAO approach• Computation: Modern research tool• Real-world materials are too

complex for class, but relevant tostudent research

• Web-based interface• Focus on physics, not computation• Future: simpler interface

http://www.wien2k.at/

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• Dispersion E(k) plots,understand direct andindirect gaps, effectivemasses etc.

• Students produce plots ofdensity of states, partialdensity of states of realmaterials

Cu3TaS4

Bandstructure; DoS computation

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Carbon Nanotubes

• Dispersion relation forgraphene

• Metallic & semiconductingNTs

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Senior Research Projects

• Start in junior year• Work with faculty & grads

- attend group meetings - hands-on in lab - present at local conferences

• Writing course in Winter of senior year - peer feedback & faculty guidance

• Write thesis• 10-minute talk in spring of senior year at

departmental Senior Thesis Conference

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Take-home message

• Explicit attention to development of professional skillsMultiple representationsActive engagementCareful attention to basics reaps rewards laterPeer-instruction and problem solvingComputation

• Curriculum:Shorter, concept-based paradigmsLonger, sub-discipline-based capstonesResearch expectation

• Solid State & NanoscienceModern examples all through curriculumSolid knowledge basisInformation is everywhere; analytical and critical thinking mustbe taught!

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Acknowledgements

• National Science FoundationDUE-0618877,-0231194,-9653250

• Oregon State UniversityDepartment of Physics,College ofScience, Academic Affairs, lots of facultytime!

• Solid State/Nano Curriculum:Janet Tate, William WarrenGuenter Schneider, David McIntyre, Henri Jansen

• Current grant PIs:Corinne A. Manogue (Director)David McIntyreTevian Dray, Barbara Edwards (Math)Emily van Zee (SMEd)

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Extra slides

27CNT-basedcoaxial cable

Rybczynski et al, APL 90, 021104 (2007)

• Co-ax cable lab teacheswave reflection at mediumdiscontinuity

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Quantum-classical connection

Tunneling through barrier

Evanescent wave inloaded string

Relevance: Magnetic tunnel junctions,STM, tunnel diodes, skin depth ….

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Multiple Representations

Can your juniors connect these? Or, given one, generatethe others? There are many, many concepts here we thinkare simple, but which most students have at best a veryfuzzy idea. If you’re afraid of the basic problem, how canyou make progress?

V!r( ) =

1

4!"0

#!r '( )

!r $!r 'dV '%

The potential at a field point P a distance r from the origin isthe sum of the potentials at that point due to each element(located at r') of the extended charge distribution.

!r '

!r P

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Spherical Harmonics in Color

•Multiple representations

Polar plot Color plot Combined plot

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