Differences between eigenstates, bound states and stationary states I am not very clear about the differences between eigenstates, bound states and stationary states.  
 A: 
*For any operator $\hat A$ an eigenstate $|\psi\rangle$ is one for which:
$$\hat A|\psi\rangle=\lambda |\psi\rangle$$
Where $\lambda$ is a constant, and is called the eigenvalue of that state. If $\hat A$ is an observable, then $\lambda$ will be real.
* A stationary state is an eigenstate of the Hamiltionain $\hat H$ (the energy operator). It is called stationary because when the system is in this state the expectation value $\langle \hat A \rangle$ of any operator $\hat A$ is time independent.
*A bound state is one that does not go to infinity and is usually $0$ outside a given range of $(x,y,z)$. An example (in 1d) would be a $$\psi=e^{-|x|}$$ Which goes to $0$ as $x\rightarrow \pm \infty$
A: *

*Eigen state : Particular to an operator, which when operates on it, gives a scalar number (or the eigenvalue) times itself.

*Stationary state : The state of a particle that does not vary with time.

*Bound state : The state of a particle bounded by within a potential, meaning - the energy of the particle in that state is less than that of the potential.

