1. Quantum Mechanics as a first physics course M. Anthony Reynolds Department of Physical Sciences 16 October 2003

2. Collaborators Tristan Hubsch, Howard University Per Berglund, University of New Hampshire

3. Birth of the “quanta” Quantum Theory was born on December 14, 1900, when Max Planck delivered his famous lecture before the Physikalische Gesellschaft (Berlin Physical Society) “Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum” “On the Theory of the Law of Energy Distribution in the Blackbody Spectrum”

4. 1875 “Physics is a branch of knowledge that is just about complete. The important discoveries, all of them, have been made. It is hardly worth entering physics anymore.” -Head of the physics department, University of Munich, to Planck at age 17

5. 1917, Nobel Prize The Nobel Prize in Physics 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta" Max Karl Ernst Ludwig Planck Germany b. 1858 d. 1947 http://www.nobel.se/physics/laureates/1918/

6. Quantum difficulty “If anybody says he can think about quantum problems without getting giddy, that only shows he has not understood the first thing about them.” - Max Planck

7. Quantum difficulty II “Anybody who thinks they understand quantum physics is wrong." - Niels Bohr

8. Quantum difficulty III “You never really know a subject unless you can prepare a freshman lecture on it.” - Richard Feynman

9. Quantum difficulty IV “You do not really understand something unless you can explain it to your grandmother.” - Albert Einstein

10. Quantum difficulty V “For an idea that at first does not look preposterous, there is no hope” - Freeman Dyson

11. Standard intro course outline Mechanics Fluids Sound Heat Electricity & Magnetism Optics Modern Physics > 125 years old!

12. Previous attempts Six Ideas that Shaped Physics –Thomas Moore Matter & Interactions –Chabay & Sherwood

13. Goals Ambitious: restructure the entire sequence –Quantum mechanics should play a fundamental role Modest: create “Physics 0” –Teach quantum first

14. Problems MATH

15. Pedagogical challenge Convey conceptual understanding without requiring the student to master all the mathematical details.

16. Approaches Historical –Newtonian mechanics, then quantum Idea-based –unifying physical concepts Deductive approach –Fundamental formulation, then classical mechanics

17. “Physics 0” Outline Qualitative overview Basic concepts (mathematical and physical) Waves Measurements Axioms of quantum mechanics Examples Classical limit

18. Qualitative overview Powers of ten, hierarchy of universe Simple vs. collective phenomena Quantitative and qualitative differences Systems of units –Including “natural”: speed-action-gravitation Order-of-magnitude

19. Basic concepts - math Limit, derivative –Product rule, chain rule Integration, anti-differentiation –Integration by parts Complex numbers »Calculus I taken concurrently

20. Basic Concepts - physics Position & time Mass vs. weight (force) Work & energy Linear momentum Action: –Potential-to-kinetic energy transfer over time –Angular momentum x rotated angle

21. Waves Plane traveling wave –not point particle Superposition (qualitative) –Wave packets –Wave-particle duality (e.g., electron diffraction) Waves (quantitative) –amplitude, wavelength, frequency –wave number, phase velocity –beats, group velocity, wave packets new paradigm

22. Measurements Probabilistic nature –Example: dice statistics Principle of complementarity (historical) –E = h –p = h/

23. Axioms  (x,t) describes object’s state (database) –Hilbert space = databank Observables are assigned real operators –Extracts values Time evolution is given by Average value is

24. Examples Quantitative –Free particle –Particle-in-a-box infinite square well Qualitative –harmonic oscillator –hydrogen atom finite square well (qualitative) elucidate strange features: wave packets, superposition, indeterminacy principle

25. Classical Limit Ehrenfest’s theorem: Computer simulations of high n states Estimate action –If, then classical physics applies

26. Ancillaries Historical digressions –How quantum physics came to viewed as correct “observe-represent-predict” cycle of modeling Symmetries Connection with current physics (e.g., strings)

27. Implementation Pilot test – Fall 2004 –ERAU –Howard University –University of New Hampshire Evaluation –pre/post test –track students through Physics I, II, III Dissemination –publish text on web (“open source”)