What would be the approach for finding the degree of time dilation for a star at any point in a general elliptical orbit around a supermassive black hole? Ideally I would be looking to work this out using the orbital parameters (semi-major axis, eccentricity and time since periapsis or equivalent...

I have seen many approaches to studying solid state physics and many of them use quantum mechanics, but why do we use it and not classical mechanics?