I am an engineering graduate..I have done vector calculus and matrix algebra. One thing that I have not understood are Eigen vectors and Eigen Values. I know how to get the answers but have NO idea what they mean. Please help me understand what they mean and how and when they should be used in applications.
Answer OK, "eigen" basically means "proper" in German. So these are solutions to the characteristtic equations of matrix algebra that you have studied.
What do they mean, physically? That they satisfy the physical conditions of the problem.
Physics seems to follow math, Einstein presciently trusted that it was not that, nor the other way around. It was that they were intertwined. Think of the concept of numbers developing, 1...2...3... these were based on physical ideas of 1...2...3...things! So math was born from observation of the physical universe. It's now considered a pure field of its own by some and a tool by others...but the two are not separated in their meaning. Nature seeks a state of balance and minimum energy, these states (when you look at solutions to wavefunctions and consider eigenvalues) are those states by definition. They are mathematically finding the minima (that process you understand from your calculus class, finding a minimum) in an equation that relates to a steady state.
I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.
I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.
Education/Credentials Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.