Abstract: We will be taking a leisurely stroll through the strange world of quantum mechanics. Starting with the historical roots of the subject, we will eventually build to an appreciation for the connection between the Fourier transform and the de Broglie wave hypothesis. Useful properties of the Fourier transform will be discussed if time permits.

This talk is intended to appeal to an audience with a broad range of mathematical experience, particularly undergraduates. That said, a familiarity with derivatives and integrals would be useful. Many pictures will be used at the onset to help illuminate the intuition behind quantum mechanics, so no formal training in advanced physics is necessary.