Recursivity in quantum mechanics

Abstract:

The techniques of effective descriptive set theory are applied to the mathematical formalism of quantum mechanics in order to see whether it actually provides effective algorithms for the computation of various physically significant quantities, e.g. matrix elements. Various Hamiltonians are proven to be recursive (effectively computable) and shown to generate unitary groups which act recursively on the Hilbert space of physical states. In particular, it is shown that the $n$-particle Coulombic Hamiltonian is recursive, and that the time evolution of $n$-particle quantum Coulombic systems is recursive.