Quantum Hamiltonians and prime numbers

Abstract

"A short review of Schrödinger Hamiltonian for which the spectral problem has beenVrelated in the literature to the distribution of the prime numbers is presented here. WeVnotice a possible connection between prime numbers and centrifugal inversions in black holes and suggest that this remarkable link could be directly studied within trapped Bose-Einstein condensates. In addition, when referring to the factorizing operators of Pitkanen and Castro and collaborators, we perform a mathematical extension allowing a more standard supersymmetric approach."