## Rayleigh-Ritz Variational Technique

A technique for computing Eigenfunctions and Eigenvalues. It proceeds by requiring

 (1)

to have a Stationary Value subject to the normalization condition
 (2)

and the boundary conditions
 (3)

This leads to the Sturm-Liouville Equation
 (4)

which gives the stationary values of
 (5)

as
 (6)

where are the Eigenvalues corresponding to the Eigenfunction .

References

Arfken, G. Rayleigh-Ritz Variational Technique.'' §17.8 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 957-961, 1985.