On the gravitomagnetic clock effect in quantum mechanics

In this article, we discuss how to carryover gravitomagnetic clock effect from classical general relativity to quantum theory and how to calculate this effect in quantum mechanics. Our calculation is valid for semi-classical regime and can be considered as the first step towards a complete gravitomagnetic quantum theory. We also show the analogy between energy levels that corresponds to the clock effect. In fact, it is argued that in quantum mechanics clock effect arises as energy level splitting in gravitomagnetic field.