In this work, we present Hamilton’s optical-mechanical analogy, which was used by Schr?dinger to obtain the famous quantum mechanics equation that bears his name. From this analogy, we show step by step how to obtain Schrodinger’s equation (time independent and dependent). Then, we discuss the meaning of the wave function and the proposed interpretations during the development of quantum theory. We also present non-diffractive solutions for the Schr?dinger equation based on solutions already known in areas such as optics and acoustics. And finally, we give some examples of other analogies that exist between optics and quantum mechanics.
Keywords
Schrödinger; Hamilton; Analogia