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

Particle waves phonon photon ??? ??? ??? electron

Electromagnetic waves

Blackbody radiation – Planck, Boltzman–Stefan, Wien energy per photon “high frequency photons cost too much energy” density of modes photons per mode

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

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