On the Derivation of the Schrodinger equation

The Schr odinger equation is one of the most vigorous achievements of physics in the twenty centuries. Unfortunately, the original derivation has not yet been fully understood since it was not established from mathematical framework of Quantum Mechanics. Perhaps, the equation in and of itself is so fundamental like the Newton's three laws of motion. In this paper, we present an approximate approach to constructing the equation by manipulating the analogue of the classical wave model and ideals of quantisation. We also explain why this derivation is only an approximation.

薛定谔方程（Schrödinger equation）是20世纪物理学最具影响力的成就之一。遗憾的是，其原始推导过程至今尚未被完全厘清，因为它并非基于量子力学（Quantum Mechanics）的数学框架所构建。该方程本身或许如同牛顿运动三定律一般，具有根本性的核心地位。本文提出一种近似方法，通过类比经典波动模型并运用量子化（quantisation）思想来构建该方程，同时阐释了为何此种推导仅为近似方法。