Is Eigenstate Same as Eigenfunction?

An eigenstate is a vector in the Hilbert space of a system, things we usually write like | >. An eigenfunction is an element of the space of functions on some space, which forms a vector space since you can add functions (pointwise) and multiply them by constants.

What is eigenstate in quantum mechanics?

An eigenstate is a quantum state whose wave function is an eigenfunction of the linear operator that corresponds with an observable. The eigenvalue of that wave function would be the quantity you observe when you measure that observable (the eigenvalue could be a vector quantity).

What is eigenvalue and eigenfunction?

Such an equation, where the operator, operating on a function, produces a constant times the function, is called an eigenvalue equation. The function is called an eigenfunction, and the resulting numerical value is called the eigenvalue.