圆柱坐标系下高阶“多项式”形式调和算子方程的分离变量解法  

A variable method of a type of equation with harmonic operator equation of high steps polynomial at cylindrical

作　　者：王春玲[1] 张改英[2] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]西安交通大学理学院,陕西西安710049

出　　处：《陕西师范大学学报（自然科学版）》2005年第3期24-26,共3页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：陕西省教育厅专项基金资助项目(04JK218)

摘　　要：对圆柱坐标系下齐次6阶“多项式”形式的调和算子方程,按本征值分15种情况分别给出了其分离变量解的具体形式,给出常数的确定方法;并将结果推广到各种非齐次情况和非轴对称情况.指出该方法也可以用于求解柱坐标系下高阶“多项式”形式调和算子方程的分离变量解,只要相应的本征值有通解表达式.According to fifteen sorts of eigenvalues, the specific solution to a type of homogeneous equation with harmonic operator of six steps polynomial in cylindrical coordinate is obtained by the variable method, and the method of determining the constant is given. Then, the work is extended to the inhomogeneous case and the non-axisymmetric case. The method can be used to solve the variable solution to a type of equation with harmonic operator of high steps polynomial in cylindrical coordinate as long as its eigenvalues have general representations.

关 键 词：调和算子 解析解 圆柱坐标 分离变量 

分 类 号：O175.4[理学—数学]