I see these terms used a lot and at times they seem to be used interchangeably. I am aware of the eigenvalue equation being applied to the normal expression of operators or their matrix versions, eg. [tex] Hu = \lambda [/tex] [tex] \lambda [/tex]u but I see this thing called u being referred to as eigenstate, eigenfunction or eigenvector (or sometimes even just vector) all the time. What's the deal with this? Thanks.