A tension in education: depth vs. breadth Sophomore physics: varies quite widely

1. First semester sophomore physics: The advantages of waves & oscillations with semi-coordinated labWalter F. Smith Physics Dept. Haverford College Haverford PAConference on Laboratory Instruction Beyond the First Year of CollegePhiladelphia, July 25, 2012

2. A tension in education: depth vs. breadth Sophomore physics: varies quite widely One common approach: Modern Physics Relativity Quantum mechanics Nuclear physics Particle physics Statistical mechanics

3. Approach to sophomore physics at Haverford College: Rigorous quantum mechanics in lecture and lab Lecture:

4. Advantages: • Quantum mechanics is very exciting to students! • Central to many hot areas of research (e.g. q. computing, q. info) • Philosophically challenging (e.g. entanglement, locality, …) • Required for many of our most impressive results (transistors, • solar power) and most important challenges • Gives students a real insight into the physics major • before they declare • Disadvantages: • Only 1-2 weeks on relativity in first 2y (during 1st-year e&m) • There are many exciting areas of physics that don’t involve q.m. http://www.latimes.com/news/science/la-sci-quantum-entanglement-20120707,0,802675.story

5. Our experience at Haverford: • Originally, students began study of quantum right after two semesters of intro • Most students struggled, achieved poor understanding • New system: • Semester 1: Waves and Oscillations • Semester 2: Quantum Mechanics • Works very well! • Increased number of majors • (~12 per year, with student • body of 1200) • Excellent, supportive • atmosphere among majors

6. Advantages of Waves & Oscillations in the sophomore year: • Important in most areas of physics • Electricity & magnetism • Anything involving quantum • Acoustics • Plasmas • Nanoscience • Provides exactly the mathematical ideas and techniques needed for quantum (and many other areas), in a less intimidating classical context • Differential equations • Complex exponentials • Matrix math • Hilbert space and orthogonal function analysis (e.g. Fourier analysis) • Eigenvalue equations • Bra-ket notation

7. Advantages of sophomore Waves & Oscillations (ctd.): • Most of material is new to students (e.g. coupled oscillators), but connected to things they’ve studied before & understand • Gives students a feeling of the challenge they will see in upper-level courses

8. Text: Connections to current research: Whale calls: Prof. Christopher Clark, Cornell Univ. Total internal reflection fluorescence microscopy: A. Gunnarson et al., Nano Letters 8, 183-188 (2008).

9. Connections to “everyday” life: Magnetic Resonance Imaging Quartz crystal from a watch Dr. Erhard Schreck

10. Web support with custom-developed applets & links to web resources Custom-developed coupled pendulum and Hilbert space applet Link to Physical Review Focus summary of Physical Review Letters paper on bat sonar Prof. Rolf Müller, Shandong Univ.

11. Bra-ket notation for coupled oscillators

12. Refreshing writing style • Humor when appropriate • Check it out Thursday in Poster Session I

13. Semi-coordinated lab: Another tension in education: creativity/exploration vs. learning the ropes • Goals of our first-semester sophomore lab: • Transition to more independent lab work: • Second semester sophomore lab • Advanced lab (junior / senior) • Research • Provide common background of experimental expertise: • Simple electronics (input & output impedance, scope operation, • op amps) • Better understanding of optics • Coherent presentation of results • Three oral reports • Two full-length written reports • Reinforcing data analysis: Uncertainty analysis, curve fitting

14. Another tension: • Challenging your students to stretch themselves • vs. Discouraging them • Oral reports: • Presentations based on data graphs, tables, • etc. (not PowerPoint) • Given to an instructor • Presentations in pairs • Typically about 30 minutes

15. Overview of the lab: • Another tension: • Reinforcing understanding vs. introducing new material • At a variety of intervals  Connected to old material • (reading, class, problem sets, • lab, exams, other courses, • research) • Using different parts of the brain • New context • Half-credit, usually taken in the same semester as the lecture component

16. First five weeks are single-week labs, done in unison by pairs, coordinated with lecture. • Week 1: Input and output impedance for DC circuits • Essential concepts for all electronics • Week 2: High- & low-pass filters • Connects to complex notation for AC circuits in lecture • Week 3: Resonant circuits • Connects to ideas in lecture • Week 4: Diodes • Crystal radio; synthesizing concepts • Week 5: Op amps • What is an amplifier? What is gain? • Feedback • The connection between a schematic & physical circuit • Debugging

17. Last 9 weeks are a series of two week labs (plus a week off!). • Done in rotation by pairs of students. • Not coordinated with lecture. • Why only semi-coordinated? • Equipment costs • Allowing students to encounter some things in lab first • Variability in timing between the lecture & lab is OK • Less sense of competition for fastest completion • Students who’ve done the lab previously help the current students, building camaraderie.

18. Dispersion relation of water waves • The beginnings of how to be • really clean • Challenging non-linear curve fitting • Dispersion relations can be • non linear

19. Torsional oscillator (TeachSpin) & coupled oscillators • Connects to key concepts from lecture • Further practice with scopes, function generators • Computer acquisition of voltages • Reinforces concepts of Faraday’s Law, and creating B with current wiki.brown.edu/confluence/display/ PhysicsLabs/Experiment+120

20. Diffraction as a Fourier transform and spatial filtering • Connection to lecture • Deeper understanding of optics • Practice thinking in reciprocal space • Simple optical design exercise: beam expander • Optical setups using research-grade components • Aspects of laser safety www.doitpoms.ac.uk/tlplib/DD1-6/image.php

21. Ultrasound imaging • Applications of wave ideas to a new context 3B Scientific

22. Shortcomings include: • Main equipment used for two of the two-week labs will never be used again. (water waves, ultrasound) • In our current version of Advanced Lab, students don’t revisit op amps. Students rarely use them in research. • Because the two-week labs are only semi-coordinated, the connection to lecture is different for different students

23. Conclusions: • Sophomore: • waves & oscillations first semester • quantum mechanics second semester • semi-coordinated labs • High level of student interest • Students know what they’re getting into when they major. • First semester labs continue building a good foundation of experimental skills and intuition. • Helpful to have a connection between lab& lecture, but exact coordination is not necessary, or even always preferred.