Definitions of eigenstate, eigenvalue and eigenfunction?

[CudBea]

Homework Statement

In quantum mechanics a physical observable is represented by an operator A.
Define the terms eigenstate, eigenvalue and eigenfunction of a quantum
mechanical operator.

Homework Equations

The Attempt at a Solution

I think I know in that eq 'f' is the eigenfunction, and lambda is the eigenvalue, but I have no idea how to write in words what they actually are, and that still leaves the question of what an eigenstate is...

Any help would be appriciated

 

[astrozilla]

The schrodinger's time independent equation can be written as Af =λf.
This means that rhe Hamiltonian(or total energy operator) operating on f gives a contant times f.This is an example of an eigenvalue equation.Solutions are an infinite set of eigenfunctions fn and associated energy eignenvalues λn.The subscript n is the quantum number.

 

[dextercioby]

First define the space (set) the operator A acts on. Then you should immediately know what 'f' stands for and what 'lambda' is. As for the <eigenstate> concept, you'd have to take the arbitrary A as the Hamilton operator for a quantum system.