Harmonic oscillators and rigid rotors

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Harmonic oscillators and rigid rotors

• Chem. 562

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Harmonic Oscillator
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Wavefunction of H.O.
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Quantum vs. classical results
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Probability distributions vs. energy
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Multi-dimensional H.O.
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Another look
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Energy quantization in 2D rotor
However, mv is not arbitrary in QM, because
lh/(mv) ? mvh/l
and l has to adopt a value such that the wave
fits on the ring!
l2pr/n ? mvh/l nh/2pr ? En2h2/(2p)2(2mr2)
n? Z
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Energy quantization in 2D rotor
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3D rotor
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Space quantization
Aligning molecules can regulate reactivities!
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3D representation
As ml increases, distribution moves towards the
x,y plane.
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3D representation
As ml increases, distribution moves towards the
x,y plane.
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Spherical Harmonics
d
p
s
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Alignment?
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The Stern-Gerlach Exp.
Kr.4d10.5s1
Otto Stern (1888-1969) Nobel prize, 1941
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Bose-Einstein Condensate
http//www.colorado.edu/physics/2000/bec/
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Bose-Einstein Condensate