Schrödinger's equation from Snell's law

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A new derivation of Schrödinger's equation is presented, based on Schrödinger's original discussions on refraction and the optical-mechanical analogy, but adopting a much simpler formalism: Newtonian mechanics and some basic elements of classical wave theory (such as Snell's law). We compare how particles and waves refract and show that the 'law of particle refraction' and the 'law of wave refraction' may become consistent if one assumes that a particle can be represented by a wave group. In this case, the differential equation whose solutions represent the waves forming such wave group is the Schrödinger equation. Due to the simplicity of the adopted mathematical formalism, we argue that this derivation can be used in quantum mechanics courses at introductory level to give students an idea of Schrödinger's original path to his wave equation.

Original languageEnglish
Article number035402
JournalEuropean Journal of Physics
Volume43
Issue number3
ISSN0143-0807
DOIs
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 European Physical Society.

    Research areas

  • quantum theory, Schrödinger equation, Snell's law, wave mechanics

ID: 303450484