Why is it that all the potentials that we use in QM are classical ?

[trosten]

Why is it that all the potentials that we use in QM are classical ? For example the columb potential. Shouldnt we use a wave equation for the potential as well as for the position?

 

[dextercioby]

Why is it that all the potentials that we use in QM are classical ? For example the columb potential. Shouldnt we use a wave equation for the potential as well as for the position?

Because it's natural..?? 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).
So everything has 'classical' roots.The notions of Hamiltonian,Lagrangian,action,field equations,energy,angular momentum,momentum,evolution operators,...Except spin.

Daniel.

 

[reilly]

Actually, in virtually any Quantum Field Theory the "potential" does obey a wave eq (like a Klein-Gordan Eq.) And, in classical E&M, potentials must be supplemented by vector potentials as well. The interaction between two charged particles is described by retarded forces/potentials, and thus requires two times. The plain fact is that the math of the retarded interaction is horribly difficult. The classical E&M potential give solvable dynamics for both classical and quantum systems. And the Coloumb Potential gives the basis in QM for a remarkably accurate description of atomic properties and dynamics.

Phenomena like the Lamb shift or the anomalous magnetic moment of the electron can be thought of as coming from a "wave description" of interactions. They involve charges absorbing radiation that the same charge emitted. QED, past lowest order approximations, is exactly a theory with interactions that can be described in terms of wave equations. But we tend not to think along those lines, and more often than not, we tend to think of QED in terms of Feynman diagrams.

Regards,
Reilly Atkinson