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In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
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Coherent state evolution for a given non usual Hamiltonian
I am trying to compute the temporal evolution of a coherent state $|\alpha\rangle$ using a given hamiltonian of the form:$$\hat{H}=\hbar \omega(\hat{a}^{\dagger}\hat{a}-\alpha(\hat{a}+\hat{a}^{\dagger …