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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.
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 ( , )
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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