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Related to eigenfunction: eigenfunction expansion


A solution of a differentiated equation that has solutions only for particular values of some parameters. Compare: eigenvalue.
[Ger. eigen, particular, peculiar to]
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We then develop the wave function, [psi], of this system with the eigenfunction [[psi].
Commonly, PSWFs are known as the eigenfunctions of Sturm-Liouville differential operator [4]:
In contrast, in paraboloidal coordinates, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is an eigenfunction of [A.
Solutions to (1) completely characterize membrane motions since the eigenfunctions form a complete orthonormal basis for the space of membrane vibrations.
i] and other parameters are known constants depending on the characteristics of a specific VSP, meaning the eigenfunction of the VSP's SWC is also a char acteristic function, like H~Q and [eta]~Q functions, representing the VSP's performance.
1] is simple and isolated and all eigenfunctions corresponding to [[lambda].
Note that different eigenvalues can have the same eigenfunction as the eigenfunctions do not depend on l.
A solution of differential equation of motion was assumed as a product of eigenfunctions of displacement and time [2, 3]:
ti] within the ith discontinuity can be expanded over the modal eigenfunction basis that satisfies the boundary conditions.
Up till now, most references to the rigorous analysis of diffraction devices have implicitly assumed infinitely periodic elements [15-18], for which the eigenfunctions are known and used in an eigenfunction expansion of the diffracted fields.