While there are conceptual and mathematical similarities between quantum mechanics and Lagrangian mechanics, it would be inaccurate to say that quantum mechanics is built directly on the principles of Lagrangian mechanics. Lagrangian mechanics is a framework used to describe the classical motion of particles and systems, whereas quantum mechanics is a fundamental theory that describes the behavior of particles at the quantum level.
Lagrangian mechanics, formulated by Joseph-Louis Lagrange in the late 18th century, provides a powerful approach to understanding classical mechanics. It introduces the concept of generalized coordinates, which can describe the configuration of a system, and the Lagrangian function, which encodes the system's dynamics. By applying the principle of least action, the equations of motion can be derived from the Lagrangian.
Quantum mechanics, on the other hand, arose in the early 20th century as a result of efforts to understand the behavior of subatomic particles, such as electrons and photons. It introduced fundamentally new concepts, such as wave-particle duality and the uncertainty principle, that have no direct analogues in classical mechanics.
However, there is a mathematical connection between the two theories. The path integral formulation of quantum mechanics, developed by Richard Feynman, involves summing over all possible paths that a particle can take to go from one point to another. These paths contribute to the probability amplitude of the particle's final state. The path integral can be related to the classical action through a process known as the Hamiltonian or Lagrangian quantization, which establishes a bridge between classical and quantum mechanics.
So while studying Lagrangian mechanics can provide a useful mathematical foundation and help in understanding some aspects of quantum mechanics, it is not a direct path to learning the intricacies of quantum mechanics itself. Quantum mechanics has its own unique principles and mathematical formalism that go beyond the scope of classical mechanics.