PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Two opposing concepts Particle theory Field theory Quantum Mechanics Position, mass, velocity, charge, spin Functions continuous in space and time

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves X1X1 X2X2 t=0 t final t final =(x 2 -x 1 )/v particle wave Mechanical Analogy of transmision

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves X2X2 t=0 t final t final =(x 2 -x 1 )/v X1X1

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves SImple Harmonic Motion  m m Equation of Motion DisplacementDisplacement x

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Wave:Wave: The propagation of a perturbation. It is also a way to transport Energy. Periodic changes in Space and Time of some Property. There is no net dosplacement of the medium The propagation of a perturbation. It is also a way to transport Energy. Periodic changes in Space and Time of some Property. There is no net dosplacement of the medium Shape of the disturbance: „Profile“ of the wave such as an instantaneous „snapshot“ of the wave form. It reoeats periodically in Time and Space. Particular „Pattern“: Sinusoidal Waves. These waves are called „Harminic Waves“. „Profile“ of the wave such as an instantaneous „snapshot“ of the wave form. It reoeats periodically in Time and Space. Particular „Pattern“: Sinusoidal Waves. These waves are called „Harminic Waves“.

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves One-Dimensional Waves – General Concepts t o x Shape of the disturbance Harmonic Waves→ Sinusoidal Waves Time, t T Temporal Period Space, x Spatial Period or Wavelength

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Space, x  p AmplitudeAmplitude PhasePhase time, t  RefFrequencyFrequency Angular Frequency Wave Number Angular Wave Number or propagation Number Angular Wave Number or propagation Number Phase Velocity Temporal Period

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Wave Function Differential Wave Equation

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Travelling Waves

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Travelling / Standing Waves Standing Waves: When the primary and reflected Waves have the same A and speed  It vibrates „in place“. Nodes: Places where the medium does not ever vibrate. When the primary and reflected Waves have the same A and speed  It vibrates „in place“. Nodes: Places where the medium does not ever vibrate.

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves The Complex Representation Complex number: Imaginary y Real x   |z| (x+i y) x=|z| cos  y=|z| sin  Euler Formula: z = |z| (cos  + isin  |z| e i  Complex Conjugate: z * = |z| (cos  - isin  |z| e -i  Wave Function:

PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves Light as an Electromagnetic Wave + E Differential Wave Equation