Annihilation vs. Creation Operators: What's the Difference?

[gerald V]

Cohererent states are defined as eigenstates of the annihilation operator. Never the creation operator is referred to.

Is this just a convention or is more behind? What is the essential difference between eigenstates of the annihilation- versus the creation operator?

Thank you very much in advance!

 

[Demystifier]

There are no eigenstates of the creation operator. The asymmetry between creation and annihilation operators stems from the fact that the ordered basis $\{|0\rangle, |1\rangle, |2\rangle,\ldots\}$ has the first element but not last element.

 

[PeroK]

What is the essential difference between eigenstates of the annihilation- versus the creation operator?

Existence!

 

[gerald V]

Got it. Thank you very much.