quantum mechanics as a first physics course m. anthony reynolds department of physical sciences 16...

Quantum Mechanics as a

first physics course

M. Anthony ReynoldsDepartment 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 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”

3

exp( / ) 1h kT

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

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/

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

Quantum difficulty II

“Anybody who thinks they understand quantum physics is wrong."

- Niels Bohr

Quantum difficulty III

“You never really know a subject unless you can prepare a freshman lecture on it.”

- Richard Feynman

Quantum difficulty IV

“You do not really understand something unless you can explain it to your grandmother.”

- Albert Einstein

Quantum difficulty V

“For an idea that at first does not look preposterous, there is no hope”

- Freeman Dyson

Standard intro course outline

• Mechanics

• Fluids

• Sound

• Heat

• Electricity & Magnetism

• Optics

• Modern Physics

> 125 years old!

Previous attempts

• Six Ideas that Shaped Physics– Thomas Moore

• Matter & Interactions– Chabay & Sherwood

Goals

• Ambitious: restructure the entire sequence– Quantum mechanics should play a fundamental

role

• Modest: create “Physics 0”– Teach quantum first

Problems

MATH

Pedagogical challenge

Convey conceptual understandingwithout requiring the student to master all the

mathematical details.

Approaches

• Historical – Newtonian mechanics, then quantum

• Idea-based– unifying physical concepts

• Deductive approach– Fundamental formulation, then classical mechanics

“Physics 0” Outline

• Qualitative overview

• Basic concepts (mathematical and physical)

• Waves

• Measurements

• Axioms of quantum mechanics

• Examples

• Classical limit

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

Basic concepts - math

• Limit, derivative– Product rule, chain rule

• Integration, anti-differentiation– Integration by parts

• Complex numbers

» Calculus I taken concurrently

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

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

newparadigm

Measurements

• Probabilistic nature– Example: dice statistics

• Principle of complementarity (historical)– E = h– p = h/

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

i Ht

h

*Q Q

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

Classical Limit

• Ehrenfest’s theorem:

• Computer simulations of high n states

• Estimate action– If , then classical physics appliesS h?

d p V

dt x

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)

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”)