Yes, quantum mechanics does require classical mechanics as a limiting case for its formulation. Classical mechanics, also known as Newtonian mechanics, describes the motion of macroscopic objects and is based on the principles of Newton's laws of motion. Quantum mechanics, on the other hand, is the branch of physics that deals with the behavior of particles at the atomic and subatomic level.
Quantum mechanics was developed in the early 20th century to explain phenomena that classical mechanics could not account for, such as the behavior of electrons in atoms and the results of experiments like the double-slit experiment. However, quantum mechanics also needed to be consistent with classical mechanics in the macroscopic regime, where classical mechanics is an excellent approximation.
Quantum mechanics is considered the more fundamental theory, as it provides a more complete and accurate description of the physical world at the microscopic level. However, classical mechanics is still widely used because it simplifies calculations and provides a good approximation for most everyday situations. In the limit of large systems or high energies, quantum mechanics reduces to classical mechanics.
The correspondence principle is an important concept in the development of quantum mechanics, which states that the predictions of quantum mechanics must approach those of classical mechanics for large systems or in the limit of large quantum numbers. This ensures that quantum mechanics is consistent with the well-established results of classical mechanics in the macroscopic world.