The derivation of the Chandrasekhar Limit involves the principles of quantum mechanics and special relativity. Chandrasekhar used the concept of electron degeneracy pressure, a quantum mechanical effect that arises from the Pauli exclusion principle, which states that no two electrons can occupy the same quantum state. As a white dwarf's mass increases, the electrons are forced into higher energy states, and their velocity approaches the speed of light, invoking relativistic effects. Chandrasekhar balanced this pressure against gravitational forces to calculate the limit.