Chet Alexander
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.
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.