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the Hydrogen Atom: A Comprehensive Review of Quantum Concepts

Explore the fundamental concepts of quantum mechanics focusing on the hydrogen atom, including eigenfunctions, rotational kinetic energy, spherical coordinates, Schrödinger’s equation, eigenvalues, and vector model of quantum angular momentum.

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the Hydrogen Atom: A Comprehensive Review of Quantum Concepts

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  1. Hydrogen Atom PHY 361 2008-03-19

  2. review of Lz operator, eigenfunction, eigenvalues rotational kinetic energy traveling and standing waves spherical coordinates definition Laplacian operator Schrödinger’s equation in spherical coordinates separation of angular variables: L2 and Lz differential equations spherical harmonics and eigenvalues vector model of quantum angular momentum radial wavefunctions effective radial potential – centrifugal `force’ radial wave functions hydrogenic orbitals Outline

  3. Spherical Coordinates

  4. Cylindrical vs. Spherical Coordinates Laplacian: Schrödinger Equation: Lz2 / 2I L2 / 2I

  5. Spherical Harmonics L2 Ylm=l(l+1)Ylm s 1 Lz Ylm= m Ylm x, y p z x, y x2+y2, xy xz, yz d 3z2-1 xz, yz x2+y2, xy f …

  6. Vector model of quantized angular momentum l = 0, 1, 2, … m = -1, -l+1, … l-1, l

  7. Radial equation – effective potential

  8. Radial hydrogenic wavefunctions

  9. Putting radial and angular parts together 2p wave

  10. Hydrogenic orbitals http://www.orbitals.com/orb/

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