Lecture_16 - Today's Lecture Quantum Mechanics and Atomic...

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1 Quantum Mechanics and Atomic Theory Today’s Lecture 12.6 Particle in a Box (optional) 12.7 The Wave Equation for the Hydrogen Atom 12.8 The Physical Meaning of a Wave Function 12.9 The Characteristics of Hydrogen Orbitals 1 The Particle in a 1D Box as a Model ± solving the Schrödinger equation for the particle in a box results 2 in many solutions (each solution consists of a wave function that is characterized by a particular value of E) ± series of quantized energy levels
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2 Solutions to the Particle-in-a-Box 3 (a) the first 3 energy levels for theparticle ina 1D box in increments of h 2 /(8mL 2 ) (b) the wave functions of the first 3 energy levels plotted as afunct ionofx (c )thesquareofthewavefunct ionsforthef irst3energy levels plotted as a function of x Wave Functions ± the wave function of a particle has no easily visualized meaning and thus a different approach was necessary ± in 1926, Max Born used classical wave theory ± in a classical wave (e.g. visible light) the amplitude of the wave corresponds to Ψ , and the intensity of the wave to Ψ 2 ± th u sf o ra ne le c t r o nw a ve ,
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3 Probability Density (or Distribution) 5 ± a final consideration of the particle-in-a-box model concerns its extension into a three-dimensional box (i.e. a case in which the particle can move in all three directions) Wave Functions of the Hydrogen Atom ± solutions of the Schrödinger equation for the hydrogen atom give the wave functions for the electron in the
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Lecture_16 - Today's Lecture Quantum Mechanics and Atomic...

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