哈密顿算符及其一般运算表达式的分析

General Expression Analysis of the Hamiltonian Operator and Its Formula

摘要: 哈密顿算符∇及其产生的拉普拉斯算符、梯度、散度和旋度常见运算式在不同曲线坐标系中具体表达式不相同。本文通过定义一个三维正交曲线坐标系(u₁, u₂, u₃)，引入坐标因子h₁、h₂、h₃，推导得到了关于∇、∇∅、∇-A、∇ΧA、∇²的一般形式及Poisson方程和Laplace方程的一般表达式。

Abstract: The Hamiltonian operator ∇ and the common expressions such as the Laplacian operator, gradient, divergence, and curl generated by it are not the same in different curve coordinate systems. This paper defines a three-dimensional orthogonal curve coordinate system(u₁, u₂, u₃), introducing coordinate factor h₁, h₂, h₃, deriving the general form of ∇, ∇∅, ∇-A, ∇ΧA, ∇², and the general expression of Poisson equation as well as Laplace equation.