Hydrogen Atom

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Hydrogen Atom

• PHY 361
• 2008-03-19

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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

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Spherical Coordinates
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Cylindrical vs. Spherical Coordinates
Laplacian
Schrödinger Equation
Lz2 / 2I
L2 / 2I
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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
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Vector model of quantized angular momentum
l 0, 1, 2, m -1, -l1, l-1, l
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Radial equation effective potential
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Radial hydrogenic wavefunctions
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Putting radial and angular parts together
2p wave
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Hydrogenic orbitals
http//www.orbitals.com/orb/