  Recently a new formulation of quantum mechanics has been suggested which is
based on the concept of signed particles, that is, classical objects provided
with a position, a momentum and a sign simultaneously. In this paper, we
comment on the plausibility of simulating atomic systems beyond the
Born-Oppenheimer approximation by means of the signed particle formulation of
quantum mechanics. First, in order to show the new perspective offered by this
new formalism, we provide an example studying quantum tunnelling through a
simple Gaussian barrier in terms of the signed particle formulation. Then, we
perform a direct simulation of the hydrogen atom as a full quantum two-body
system, showing that the formalism can be a very promising tool for
first-principle-only quantum chemistry.
