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lecture_19 - CHAPTER 7 The Hydrogen Atom 7.1 Application of...

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    7.1 Application of the Schrödinger Equation to the Hydrogen Atom 7.2 Solution of the Schrödinger Equation for Hydrogen 7.3 Quantum Numbers 7.4 Magnetic Effects on Atomic Spectra – The Normal Zeeman Effect 7.5 Intrinsic Spin 7.6 Energy Levels and Electron Probabilities CHAPTER 7 The Hydrogen Atom The Hydrogen Atom The atom of modern physics can be symbolized only through a partial differential equation in an abstract space of many dimensions. All its qualities are inferential; no material properties can be directly attributed to it. An understanding of the atomic world in that primary sensuous fashion…is impossible. - Werner Heisenberg
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    Application of the Schrödinger Equation The potential (central force) V ( r ) depends on the distance r between the proton and electron. Transform to spherical polar coordinates because of the radial symmetry. Insert the Coulomb potential into the transformed Schrödinger equation.
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    Application of the Schrödinger Equation The wave function Ψ is now a function of ( r , θ, φ ) . Equation is separable. Solution may be a product of three functions. By this substitution we may be able to separate the Schrodinger equation into three separate differential equations, each depending on one coordinate: r , or .
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    Solution of the Schrödinger Equation Principal quantum number n = 1,2,3,… Orbital quantum number l = 0,1,2,…,(n-1) Magnetic quantum number m l = 0, ± 1, 2,…, l g ( φ ) = Ae im l f lm l ( θ ) R nl ( r ) Y lm l ( , )
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    Principal Quantum Number The solution to the radial equation requires that E be positive (ionized atom) or have one of the negative values E n (signifying that the electron is bound to the atom) specified by Classical model of the atom (solar system): total energy can have any value. If the planet is trapped permanently in the solar system, the energy is negative .
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    Orbital Quantum Number Look again at the radial equation This equation is concerned with the radial motion. However,
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This note was uploaded on 04/15/2008 for the course PHY 361 taught by Professor Alarcon during the Spring '08 term at ASU.

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lecture_19 - CHAPTER 7 The Hydrogen Atom 7.1 Application of...

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