![J=int_a^b[p(x)y_x^2-q(x)y^2]dx](/images/equations/Rayleigh-RitzVariationalTechnique/NumberedEquation1.svg) |
(1)
|
具有平稳值，并服从归一化条件
 |
(2)
|
和边界条件
 |
(3)
|
 |
(4)
|
它给出了
![F[y(x)]=(int_a^b(py_x^2-qy^2)dx)/(int_a^by^2wdx)](/images/equations/Rayleigh-RitzVariationalTechnique/NumberedEquation5.svg) |
(5)
|
的平稳值，为
![F[y_n(x)]=lambda_n,](/images/equations/Rayleigh-RitzVariationalTechnique/NumberedEquation6.svg) |
(6)
|
Rayleigh-Ritz 变分法
是对应于
。使用 Wolfram|Alpha 探索
参考文献
Arfken, G. "Rayleigh-Ritz 变分法。" §17.8 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 957-961, 1985.Rayleigh, J. W. "关于寻找风琴管开口端修正的方法。" Phil. Trans. 161, 77, 1870.Ritz, W. "关于求解数学物理中某些变分问题的新方法。" J. reine angew. Math. 135, 1-61, 1908.Whittaker, E. T. and Robinson, G. "最小化问题的 Rayleigh-Ritz 方法。" §184 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 381-382, 1967.在 Wolfram|Alpha 中被引用
Rayleigh-Ritz 变分法引用为
Weisstein, Eric W. "Rayleigh-Ritz 变分法。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/Rayleigh-RitzVariationalTechnique.html