Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Abstract
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I refer to this method as a guided numerical approximation scheme and it is based upon a new look at what the path integral tells us about states in Hilbert space. I begin with simple exactly solvable models and show how to handle problems which cannot be dealt with analytically, this includes the treatment of the evolution of a Gaussian wave-packet in an anharmonic potential as well tunneling problems (i.e., instanton effects)
Cite
@article{arxiv.0902.1775,
title = {Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations},
author = {Marvin Weinstein},
journal= {arXiv preprint arXiv:0902.1775},
year = {2009}
}
Comments
Invited Talk Light Cone 2008. 11 pages, no figures, link to web site where the reference animations can be viewed