Hydrogen Atom - PowerPoint PPT Presentation

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Hydrogen Atom

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rotational kinetic energy. traveling and standing waves. spherical coordinates. definition ... vector model of quantum angular momentum. radial wavefunctions ... – PowerPoint PPT presentation

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Title: Hydrogen Atom


1
Hydrogen Atom
  • PHY 361
  • 2008-03-19

2
Outline
  • review of Lz
  • operator, eigenfunction, eigenvalues
  • rotational kinetic energy
  • traveling and standing waves
  • spherical coordinates
  • definition
  • Laplacian operator
  • Schrödingers 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

3
Spherical Coordinates
4
Cylindrical vs. Spherical Coordinates
Laplacian
Schrödinger Equation
Lz2 / 2I
L2 / 2I
5
Spherical Harmonics
L2 Ylml(l1)Ylm
s
1
Lz Ylm m Ylm
x, y
p
z
x, y
x2y2, xy
xz, yz
d
3z2-1
xz, yz
x2y2, xy
f
6
Vector model of quantized angular momentum
l 0, 1, 2, m -1, -l1, 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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