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Home > 2011 Mathematical Art Exhibition


"Gaussian Wave Packet Sculpture," by Chet Alexander (University of Alabama, Tuscaloosa)

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 wavepacket model of a particle in quantum mechanics. This is accomplished by forming a linear combination of plane waves of different wavenumbers, 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[(xx_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[(kk_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


