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  • Atkins Physical ChemistryEighth EditionChapter 9Quantum Theory:Techniques and ApplicationsCopyright 2006 by Peter Atkins and Julio de Paula

    Peter Atkins Julio de Paula

  • Chap 9Quantum Theory: Techniques and ApplicationsObjectives:

    Solve the Schrodinger equation for:

    Translational motion (Particle in a box)Vibrational motion (Harmonic and anharmonic oscillator)Rotational motion (Particle on a ring & on a sphere)

  • Fig 9.1 Particle in a one-dimensional box Particle is not free

    For acceptable , boundary conditionsmust be set:

    must vanish at x = 0 and x = L

    Implies quantization!

  • Fig 9.2 Allowed energy levels for a particle in a one-dimensional boxNormalized wavefunction:n = 1, 2, 3, n 0 so:is called the zero-point energy

  • Fig 9.3 First five normalized wavefunctions of PIB0L

  • Fig 9.4 First two normalized wavefunctions of PIBwith probability distributions

  • Real world PIB: a delocalized electronin a conjugated system1 -Carotene

  • Correspondence Principle:

    Classical mechanics emerges from quantum mechanics as high quantum numbers are reached

    i.e., particle may be found anywhere as n

  • Fig 9.5 Probability of two wavefunctions1 and 3 areorthogonalororthonormalIn Bra-ket notation:

    1|3 = 0 when n n'

  • Fig 9.6 Two dimensional square well

  • Fig 9.7 Contours for particle in 2-D rectangular welln1 = n2 =1n1 = 1, n2 =2n1 = 2, n2 =1n1 = 2, n2 =2

  • Fig 9.8 Contours for particle in 2-D square surfaceHere, L1 = L2 = Lare said to be degenerate

  • Fig 9.9 Tunnelling of a particle through wall when V < Leakage by penetration through a classically forbidden region

  • Fig 9.13 Wavefunction of a heavy particle decays morerapidly than that of a light particle Light particles havehigher probability oftunnelling

  • TunnelingChemical effects of tunneling:

    Isotope-dependence of reactions rates

    Transfer of a proton in an acid-base reaction

    Mechanism of enzyme-catalyzed reactions

    Electron transfer in redox reactions

    Scanning tunneling microscopy (STM)

  • Fig 9.16 Tip of a Scanning Tunnelling Microscope (STM)Pt-Rh or WUltrahighvacuum

  • Title : The Making of the Circular Corral Media : Iron on Copper (111) We can predict what goes on in the corral by solving the classic eigenvalueproblem in quantum mechanics -- a particle in a hard-wall circular box.

  • Title : Stadium Corral Media : Iron on Copper (111)

  • *************

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