  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.
