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Is there a mathematically rigorous book that covers both classical and quantum mechanics? If so, what is the book?
Classical mechanics is the study of the motion of macroscopic objects, while quantum mechanics is the study of the behavior of microscopic particles. Classical mechanics follows deterministic laws, while quantum mechanics involves probabilistic behavior. Additionally, classical mechanics can be described using continuous variables, while quantum mechanics uses discrete quantities.
Quantum mechanics takes into account the wave-particle duality of matter, which is not accounted for in classical mechanics. It also explains phenomena such as quantum tunneling and wave interference, which cannot be explained by classical mechanics. Therefore, quantum mechanics is considered to be more accurate in describing the behavior of matter at a microscopic level.
Yes, classical and quantum mechanics can be applied to the same systems, but they provide different levels of accuracy. Classical mechanics is a good approximation for macroscopic objects, while quantum mechanics is necessary for accurate predictions at the microscopic level. In some cases, classical mechanics can also be derived from quantum mechanics as a limiting case.
The key principles of quantum mechanics include superposition, uncertainty principle, and wave-particle duality. Superposition states that a system can exist in multiple states simultaneously, uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty, and wave-particle duality states that all particles have both wave-like and particle-like properties.
The Schrödinger equation is the fundamental equation of quantum mechanics, which describes the time evolution of a quantum system. It is used to calculate the probability of finding a particle in a certain state at a given time. It takes into account the potential energy of the system and the wave function of the particle, and can be solved to determine the allowed energy levels of a system.