物理
类比
经典力学
形式主义(音乐)
薛定谔方程
薛定谔猫
斯奈尔定律
波动方程
自由粒子
微分方程
物理定律
折射
数学物理
量子力学
量子
音乐剧
视觉艺术
艺术
哲学
语言学
作者
Nathan Willig Lima,Ricardo Karam
标识
DOI:10.1088/1361-6404/ac5635
摘要
Abstract 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.
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