Light behaves as both a wave and a particle at the same time!

Wave Particle Duality

PARTICLE properties individual interaction dynamics: F=ma mass – quantization position(time) – localized mass spin

COMMON properties: energy, momentum, velocity

WAVE properties collective interference – superposition dynamics: wave equation standing waves – modes wavelength (freq) – periodic dispersion polarization

reflection, refraction, trans. diffraction – Huygens

Reflection, Diffraction, Interference animation

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Particle waves

phonon

photon

electron??? ??? ???

Electromagnetic waves

Blackbody radiation – Planck, Boltzman–Stefan, Wien

densityof modes photons per mode

“high frequencyphotons cost toomuch energy”

energy per photon

Photoelectric effect – Einstein

X-rays – Roentgen, Bragg, Laue, Duane-Hunt, Compton

Particle Waves – de Broglie, Davisson-Germer

Wave packets – Fourier, Heisenberg

Hydrogen atom – Rutherford, Bohr

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Potential wells – conservation of energy

Schrödinger Equation

operators

tunneling

See reviews of Exams II, III

Separation of variables

Hydrogen atom

Angular momentum J = L + S

Pauli exclusion principle

Multi-particle wave function• atoms• molecules• crystals

Statistical mechanics• degeneracy• Maxwell-Boltzman, Bose-Einstein, Fermi-Dirac distributions