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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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Expanded versions of ten lectures delivered at the University of Kentucky in June 2011 introduce the quantum mechanical interpretation of eigenfunctions and their time evolution, the oscillation and concentration of an orthonormal basis of eigenfunctions, and the properties of eigenfunctions of the Laplace operator and of Schr|dinger operators.
In the paragraph about the eigenfunctions in the presence of a magnetic field, which I gave you to read a few days before you left Copenhagen, I had tried to prove; that these functions for arbitrary velocities were those where [[psi].
Moreover, in [5] is was found that PSWFs are also the eigenfunctions of the following integral equation:
To obtain the mode numbers p and q and the eigenfunctions, modified Bolotin method is used.
k,l,m](r,[theta],[phi]), and spheroconical [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are eigenfunctions of operator [L.
The general solution to (18) is linear combination of both eigenfunctions
where [lambda] are the eigenvalues and u(x, y) are the eigenfunctions.
Wu, Dissipative non-self-adjoint Sturm-Liouville operators and completeness of their eigenfunctions, J.
are the eigenvalues and eigenfunctions of the boundary value problem (8) with the boundary condition
1] is simple and isolated and all eigenfunctions corresponding to [[lambda].
It's intended for use as a two-semester course of study, can be used either by professors as a sourcebook for lecture materials or by students pursuing courses in quantum mechanics, and it discusses different approaches to calculation from Born series and approximations to what happens in the case of degenerate unperturbed eigenfunctions.