First semester sophomore physics: The advantages of waves & oscillations with semi-coordinated labWalter F. Smith

Physics Dept. Haverford College Haverford PA

Conference on Laboratory Instruction Beyond the First Year of CollegePhiladelphia, July 25, 2012

A tension in education: depth vs. breadth

Sophomore physics: varies quite widely

One common approach: Modern PhysicsRelativityQuantum mechanicsNuclear physicsParticle physicsStatistical mechanics

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

Lecture:

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

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

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

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

Text: Connections to current research:Whale calls:

Total internal reflection fluorescence microscopy:Prof. Christopher Clark, Cornell Univ.

A. Gunnarson et al., Nano Letters 8, 183-188 (2008).

Connections to “everyday” life:

Magnetic Resonance Imaging

Quartz crystalfrom a watch

Dr. Erhard Schreck

Web support with custom-developedapplets & links to web resources

Custom-developedcoupled pendulumand Hilbert spaceapplet

Link to Physical Review Focus summary of Physical Review Letterspaper on bat sonar

Prof. Rolf Müller, Shandong Univ.

Bra-ket notation for coupled oscillators

•Refreshing writing style•Humor when appropriate

•Check it out Thursday in Poster Session I

Semi-coordinated lab:

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

Another tension in education: creativity/exploration vs. learning the ropes

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

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

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

lectureWeek 3: Resonant circuits

• Connects to ideas in lectureWeek 4: Diodes

• Crystal radio; synthesizing conceptsWeek 5: Op amps

• What is an amplifier? What is gain?• Feedback• The connection between a schematic & physical

circuit• Debugging

•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.

•Dispersion relation of water waves• The beginnings of how to be

really clean• Challenging non-linear curve fitting• Dispersion relations can be

non linear

•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

•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

•Ultrasound imaging• Applications of wave ideas to a new context

3B Scientific

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

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.