Bohr’s correspondence principle says that if a new theory (quantum mechanics) is valid, it must give the same correct results as the old theory, i.e., it must correspond, in any area where the old theory (classical mechanics) has been verified.
Work Step by Step
Classical mechanics and quantum mechanics overlap for "medium-size" systems: a collection of particles that is large enough for classical physics to be applied, yet small enough that quantum effects are still observable. This happens when the de Broglie wavelength is small when compared to the dimensions of the system itself. This is discussed on page 611.