A DERIVATION OF SCHRÖDINGER'S EQUATION BY USING CHARACTERISTIC FUNCTION METHOD

以特徵函數推導薛丁格波動方程式之研究

Yaw-Dong Shih(史耀東)

《大同學報》 38期 (2024/01) Pp. 65-67+81

摘要

The equations of de Broglie's matter waves, are derived through the relativistic energy-momentum relation. The equations of matter wave function are transformed in between the stationary reference system of coordinates and moving reference system of coordinates through the function of Lorentz transformation. The equations of de Broglie's matter waves are then expanded with mass m in power series of v^2/c^2 to be analyzed. In order that the equations of matter waves to have a nonzero solution for the homogeneous equations, a special pair of characteristic equations located at such somewhere that its order of magnitude are satisfied to be a solution in ordinary scale, and it happens to be the Schrödinger's Equation. The de Broglie's equation of matter waves also can apply to a photon particle, in this situation, 2𝑚_0 the mass in Schrödinger's Equation is replaced by the photon's inertial mass m, the kinetic energy of the photon.

關鍵字

Schrödinger's equation ； characteristic function

並列摘要

首先迪布羅伊物質波動函數的兩個方程式，經由相對性能量與動量的基本方程式推導出來，此物質波的波動函數在靜態參考座標系與移動參考座標系之間的轉換可透過羅倫茲座標轉換函數來完成。接著，迪布羅伊的兩個物質波函數方程式裏的質量以v^2/c^2的乘方被展開成為級數，以此來分析齊次物質波函數方程式非零解所需要的條件，並以此獲得一組位於某個特殊位階的乘方所展開的特徵偏微分方程式，而此所在之處正是薛丁格方程式。迪布羅伊的兩個物質波函數方程式亦可適用於電磁波的光子，在這個類薛丁格方程式之中，光子以其既是全能量也是動能的慣性質量m，取代在薛丁格方程式中的2𝑚_0。

並列關鍵字

薛丁格波動方程式 ； 特徵函數