How is an arbitrary operator usually denoted in quantum mechanics?

Question

Which symbols are usually used to denote an arbitrary operator in quantum mechanics, such as O in the following example?

$O \mbox{ is Hermitian} \Leftrightarrow \Im{\left< O \right>} = 0$

Answer 1

It's common to put a hat over anything that's an operator instead of a c-number, so that $\hat A$ is an operator, $A$ is a c-number. Then we can use any letter as either an operator or as a c-number. Your $\hat O$ or $O$ to some extent suggests something that is specifically an observable quantity, just as $\hat H$ suggests a Hamiltonian operator, although one would usually expect such uses to be explicitly stated.

At the end of the day, however, it's a matter of art to get a paper to look recognizably like the other papers in a field. The use of a particular symbol for a particular purpose can come almost to define a particular area of Physics, and people in that field may stop reading a paper for flagrantly breaking such a rule unless a good enough reason is given for doing something else. To have those nuances down pat requires that you read enough papers in the field you want to write in carefully enough to notice what is used consistently for what.

Answer 2

In my experience, which covers basic QM and quantum field theory to some extent, people tend to use $A$ or $O$ for a generic operator. The convention that $O$ indicates an observable is not universal - at least, not universally used, although it's probably at least familiar to most physicists. (Same with the hat convention that Peter mentioned; everyone understands it but not everyone uses it all the time.)

If a paper refers to multiple generic operators, then it's typical (again, in my experience) to denote them using sequential letters starting from $A$. So for example, one might talk about a commutator $[A,B]$ or $[[A,B],C]$ or something like that. Other than that, though, I would consider it unusual to see letters other than $A$ or $O$ used to denote generic operators.