I'm a little bit confused in general about what an eigenstate is. So say we have something like: H|n>=hw(N+1/2)|n> |n> is the eigenket, hw(N+1/2) is the eigenvalue, but what exactly is an eigenstate? The entire question asks if there are eigenstate to the creation operator and to prove it. I thought that a*|n>=sqrt(n+1)|n+1> Isnt that the eigenstate? I guess I'm pretty lost in general. Any help would be appreciated.