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Is there a difference between "eigenfunction" and "eigenstate"? They seem to be used interchangeably in texts, which is confusing. My guess is that an "eigenfunction" has an explicit representation/argument, e.g. in terms of position, $x$, whereas an "eigenstate" is abstract. Thanks in advance for any clarification! :) But then again, some texts violate this rule, so I'm prolly wrong... |
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Maybe in principle, not really in practice. Most people talking casually will use the interchangeably. If you want a rule that makes sense though, "states" are what we call the objects that live in a hilbert space (we also call them vectors, thus eigenvectors!) so the generic, "coordinate-independent" ket should be the eigenstate. It's projection onto a definite coordinate basis (say space or momentum) then becomes a mathematical function of that coordinate, so we should call that guy the eigenfunction (which then becomes a basis dependent notion) |
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