Rayleigh-Ritz Variational Technique
A technique for computing eigenfunctions and eigenvalues. It proceeds by requiring
![J=int_a^b[p(x)y_x^2-q(x)y^2]dx](/National_Library/20161007105358im_/http://mathworld.wolfram.com/images/equations/Rayleigh-RitzVariationalTechnique/NumberedEquation1.gif) |
(1)
|
to have a stationary value subject to the normalization condition
 |
(2)
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and the boundary conditions
 |
(3)
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This leads to the Sturm-Liouville equation
 |
(4)
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which gives the stationary values of
![F[y(x)]=(int_a^b(py_x^2-qy^2)dx)/(int_a^by^2wdx)](/National_Library/20161007105358im_/http://mathworld.wolfram.com/images/equations/Rayleigh-RitzVariationalTechnique/NumberedEquation5.gif) |
(5)
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as
![F[y_n(x)]=lambda_n,](/National_Library/20161007105358im_/http://mathworld.wolfram.com/images/equations/Rayleigh-RitzVariationalTechnique/NumberedEquation6.gif) |
(6)
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where 
are the
eigenvalues corresponding to the eigenfunction 
.
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