The discussion centers on the use of classical potentials, such as the Coulomb potential, in Quantum Mechanics (QM). It highlights that while QM employs classical Hamiltonian observables, the second principle of QM allows for quantization of these observables into self-adjoint operators on Hilbert spaces. Notably, in Quantum Field Theory, potentials can indeed follow wave equations like the Klein-Gordon equation. The conversation also touches on the complexities of retarded interactions in classical electromagnetism and their implications for quantum systems, including phenomena like the Lamb shift and the anomalous magnetic moment of the electron.
PREREQUISITESPhysicists, quantum mechanics students, and researchers interested in the foundational aspects of quantum theory and the interplay between classical and quantum potentials.
trosten said:
It's the idea of quantization.Describing interactions at quantum level by means of mathematical objects requiredby the formalism of QM.The second principle of QM (the postulate of quantization) says that for observables with classical correspondent (the spin angular momentum is an example of quantum observable which does not have classical correspondent) we do the quantization by passing all classical Hamiltonian observables viewed as functions from the Poisson algebra of Hamiltonian observables into densly defined self adjoint linear operators acting on th separable Hilbert space of states (defined in the first principle/postulate).