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QUANTUM MECHANICS Matter Waves 1. De Broglie and Schrodinger 2. Electron microscopes 3. Quantum Tunneling (microscopes) Matter Waves Everything (photons, electrons, SMU students, planets, ..) has a probability wave - de Broglie Wavelength λ = h = Planck’s constant p momentum Q. What is your wavelength? Electron Waves A. About 10-35 m (Practically Unobservable) But… photons, electrons, other elementary particles can have very small p, hence observable wavelength Schrodinger’s Equation • Based on Conservation of Energy principle • Describes how probability waves move • Output is `wavefunction’ Ψ - height of the wave at any one place and time (probability is Ψ2) • Visible light -> Microscopes use lenses and mirrors to guide • Electrons -> Electron microscopes use electricity to guide Momentum larger than for visible photons, wavelength smaller, see more details E.g. cancer cell Hypodermic needle Velcro Staple Spider’s foot Mascara brush Dental drill tip Energy Barriers Classical physics – Energy needed to surmount barrier Quantum Physics – Small probability to pass through Waves can pass through `forbidden’ regions Quantum wave exists within and beyond energy barrier Probability to `tunnel’ through grows rapidly as width/height of barrier decreases QM applies to everything … including you Very (very) small probability that you can walk through walls Scanning Tunneling Microscope (STM) • Electrons quantum tunnel from tip to sample through (air) barrier • Tunneling rate (current) extremely sensitive to tip-sample separation • Measured current provides topographical map of sample surface Particle Colliders Accelerate to very large p and collide Quark particles “Image” smallest, simplest things known Elementary particles – characterized by a few numbers Atlas Detector E.g. Large Hadron Collider