The Symplectic Egg (1208.5969v1)

Abstract: We invite the reader (presumably an upper level undergraduate student) to a journey leading from the continent of Classical Mechanics to the new territories of Quantum Mechanics. We'll be riding the symplectic camel and have William of Occam as travel companion, so no excess baggage is allowed. The first part of our trip takes us from the symplectic egg to Gromov's non-squeezing theorem and its dynamical interpretation. The second part leads us to a symplectic formulation of the quantum uncertainty principle, which opens the way to new discoveries.