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It is apparent to anyone who thinks about it that, to a large degree, thebasic concepts of Newtonian physics are quite intuitive, but quantum mechanicsis not. My purpose in this talk is to introduce you to a new, much moreintuitive way to understand how quantum mechanics works. I refer to this methodas a guided numerical approximation scheme and it is based upon a new look atwhat the path integral tells us about states in Hilbert space. I begin withsimple exactly solvable models and show how to handle problems which cannot bedealt with analytically, this includes the treatment of the evolution of aGaussian wave-packet in an anharmonic potential as well tunneling problems(i.e., instanton effects)

Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations