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Static Potentials and Eigenstates Classical Particle in a Box Quantum Particle in a Box: The Infinite Square Well Particle in an Infinite Square Well: The Wavefunction The Probability Density The Harmonic Oscillator Potential The Harmonic Oscillator Energy Levels The Harmonic Oscillator Wavefunctions for the First Four Energy Levels The Harmonic Oscillator Probability Densities for the First Four Energy Levels The Harmonic Oscillator Probability Density and the Approach to Classical Behavior for Large n Local Minima in Complicated Potentials May Be Approximated as Harmonic Oscillators Particle From the Left Tunneling Through a Potential Barrier A T A T A T A T A T A T A T Matter as a Wave • Originally postulated by de Broglie in 1924 – NO evidence at this point – He surmised that l=h/p: E=1/2 mv2=p2/2m • Davison-Germer (1924) – Electron diffraction – Found by accident (“faulty” nickel target) – “ruined” Germer’s second honeymoon • G.P. Thompson – Went through the crystal Light as a Particle •Light of very low intensity – can see single “particles” that DO have momentum hit screen •Eventually the expected double slit diffraction pattern emerges •Light consists of photons (massless particles) – originally postulated by Einstein •Ephoton=hf=hc/l •h=6.63x10-34 Js (Planck’s constant) Particle Waves ln=2L/n Since l=h/mv, vn=nv1 v1=h/(2Lm) En=½mvn2 En=n2E1 E1=h2/(8mL2) Me: l=10-34 m, E1=10-38 J, n=1035 (n BIG, classical) Electrons not!!! Spectrometer The end of the 19th century – towards the slow death of classical physics A T