I'm learning the basics of quantum mechanics and just started learning about the various pictures of quantum mechanics. The general form of the Heisenberg equation of motion is $$\frac{d}{dt}A(t) = \frac{i}{\hbar}[H(t),A(t)] + \left(\frac{\partial A}{\partial t}\right)_H$$ where $A$ is the operator in the Schrodinger picture and $A(t)$ is the time dependent version of $A$ which is defined by $$A(t) = U(-t)AU(t).$$ I understand how this equation is derived from the Schrodinger equation for the time evolution operator, but my confusion is with the term $\left(\frac{\partial A}{\partial t}\right)_H$ on the right. I know generally that it captures "explicit dependence" on time, but I'm not really sure what this really means. I was under the impression that operators should not explicitly depend on time in the Schrodinger picture, so I'm not sure what exactly this term is capturing and why it is necessary. I was wondering if someone has a concrete example of how this term comes into play.
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