# Chet Alexander

Professor Emeritus
Department of Physics and Astronomy, University of Alabama
Tuscaloosa. Alabama

I am continuing to create sculptures that recognize and appreciate the work of scientists and mathematicians whose remarkable insight has given us many physical and theoretical models of our world. My sculptures represent these models, as well as sculptures of the persons themselves. Previously created sculptures have referenced the work of sixteen different scientists and mathematicians, and I have attempted to make the details of these sculptures as true as possible to the actual physical and theoretical models. Many of the sculptures are based on mathematical calculations, and some require light sources for observation.

The media for my sculptures have included wood, bronze, aluminum, brass, copper, Plexiglas, graphite and plaster. I have used the lost-wax method for bronze and aluminum sculptures as well as wood turning and carving and metal joining techniques. Gaussian Wave Packet Sculpture
9" x 11" x 10"
Wood ( birch, walnut, maple, ebony)
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 x0. The probability of finding the particle at position x0 is given by the probability density of the particle as

ІΨ(x,0) І^2~exp][-(x-x0)^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-k0)^2/2(∆k)^2]

The wave packet sculpture presents a Gaussian wave packet envelope and an electromagnetic wave enclosed in the envelope.