Eigenstate vs. Eigenfunction — What's the Difference?

One of a set of quantum-mechanical descriptions of the possible state of a physical system, using the mathematics of eigenvectors and generally existing in a state of superposition until the moment of observation.

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as for some scalar eigenvalue λ.

(physics) A dynamic quantum mechanical state whose wave function is an eigenvector that corresponds to a physical quantity

(mathematics) A function $\backslash phi$ such that, for a given linear operator $D$, $D\backslash phi=\backslash lambda\backslash phi$ for some scalar $\backslash lambda$ (called an eigenvalue). Category:en:Functions