Physics major schedule

They are quite independent - classical mechanics will teach you how to work with Lagrangian's and Hamiltonian's which are required for quantum mechanics; you will do a lot of partial derivatives, and hopefully learn about the calculus of variations.

Modern physics will cover a lot of - surprise! - modern physics! But it will emphasize the _physics_ and not the abstract calculations that are required for analytical mechanics or quantum mechanics. You should learn about quanta from the earliest physical experiments such as the photoelectric effect, the idea of photons, how a laser works, atomic spectra, electronic transitions, etc -- then some nuclear physics (E=mc^2 and more), and some relativity. It can be a great class.

I don't see a problem taking both as long as you are not otherwise overloaded.

 

It's typical for a physics student to concurrently take classes that focus on completely different areas and scales. It can be a bit mind-bending but you'll adjust.

 

Atomic physics, Particle physics and Condensed Matter physics are given in the same semester, atleast in my country.