is that eigenvector is (linear algebra) a vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context while eigenstate is (physics) a dynamic quantum mechanical state whose wave function is an eigenvector that corresponds to a physical quantity.

What is an eigenstate and eigenvalue?

Consider a general real-space operator, A(x). When this operator acts on a general wavefunction ψ(x) the result is usually a wavefunction with a completely different shape. ... These special wavefunctions are called eigenstates, and the multiples are called eigenvalues.

Is eigenfunction the same as eigenvector?

An eigenfunction is an eigenvector that is also a function. Thus, an eigenfunction is an eigenvector but an eigenvector is not necessarily an eigenfunction. For example, the eigenvectors of differential operators are eigenfunctions but the eigenvectors of finite-dimensional linear operators are not.