1 / 27

Quantum Mechanics as a first physics course

Quantum Mechanics as a first physics course. M. Anthony Reynolds Department of Physical Sciences 16 October 2003. Collaborators. Tristan Hubsch, Howard University Per Berglund, University of New Hampshire. Birth of the “quanta”. Quantum Theory was born on December 14, 1900, when

vickier
Download Presentation

Quantum Mechanics as a first physics course

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. 1858d. 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 andphysical) • 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 new paradigm • 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

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

  23. Axioms • Y(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”)

More Related