Download Quantum mechanics is the physics of the small, such as electrons

Quantum Mechanics and its Linear Algebra Influence
By: Mandy Switzer
Quantum mechanics is the physics of the small, such as electrons, protons,
neutrons, and photons. With quantum mechanics, one can more easily and more
correctly see how and why particles behave a certain way, which was very difficult using
classical physics. This branch of physics uses the mathematics and techniques of linear
algebra to solve many types of problems and actually led to the breakthrough of
Schrodinger’s Equation and other ideas. Matrix properties are used for operators such as
position and momentum and help make the mathematics correct when normal
multiplication failed. Rotation, projection, and translation matrices are used for the
visualization and movement of particles. Also, eigenvalues and eigenvectors are used in
Schrodinger’s Equation.
I will show how matrices are transformed into quantum mechanic “language” and
how they are used. I will also show how eigenvectors and eigenvalues come into play in
Schrodinger’s Equation and how operators behave just like matrices in linear algebra.
Preliminary List of References:
http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/quanmath/matrix.
htm
http://www.aip.org/history/heisenberg/p07b.htm
http://math.ucr.edu/home/baez/lie/node12.html
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/eigen.html
http://en.wikipedia.org/wiki/Wave_mechanics