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 The connection between mathematics and
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used in the design of Gothic cathedrals, Rose windows,
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and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius bands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.
Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.
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Home > 2011 Mathematical Art Exhibition
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"Gaussian Wave Packet Sculpture," by Chet Alexander (University of Alabama, Tuscaloosa)
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Wood (birch, walnut, maple, ebony), 9" x 11" x 10", 2006
Mathematics of the Wave -Packet Sculpture:
In this sculpture, mathematics was used to calculate the Gaussian wave-packet model of a particle in quantum mechanics. This is accomplished by forming a linear combination of plane waves of different wave-numbers, k. A particle with mass and momentum p can have wave properties as described by the de Broglie wavelength relation λ=h/p. The Gaussian wave packet model is a way to combine the wave and particle properties of a particle of momentum p=hk localized at position x_0. The probability of finding the particle at position x_0 is given by the probability density of the particle as
ІΨ(x,0) І^2~exp[-(x-x_0)^2/2(∆x)^2]
, and by a Fourier transform the probability density of the particle's momentum can be written
ІΨ(k) І^2~exp[-(k-k_0)^2/2(∆k)^2].
The wave packet sculpture presents a Gaussian wave packet envelope and an electromagnetic wave enclosed in the envelope. --- Chet Alexander
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