So, after all, what is the meaning of “a quantum eigenstate”?
One way to resolve the circular definition is to define
a definite state
a state whose measurement result can be predicted with 100% certainty provided that the initial condition is given with 100% accuracy
Another way to resolve the circular definition is to realize that
1. a classical state, as a macroscopic definite state, is experimental or observational;
2. a quantum eigenstate, as a microscopic definite state, is conceptual.
A classical state is what we, as macroscopic observers, can see directly.
A quantum eigenstate is what we cannot see. Moreover, it is not absolute. For the same system, there are more than one choice of state vector bases, in the sense that different sets of measurements can get different sets of eigenstates.
The concept of “quantum eigenstates” exists because we insist to express quantum states in terms of daily-life (classical (macroscopic) physics) language.
2013.06.22 Saturday (c) All rights reserved by ACHK