  We regard the cosmological fluid within an exponentially expanding FLRW
spacetime as the probability fluid of a nonrelativistic Schroedinger field. The
scalar Schroedinger particle so described has a mass equal to the total
(baryonic plus dark) matter content of the Universe. This procedure allows a
description of the cosmological fluid by means of the operator formalism of
nonrelativistic quantum theory. Under the assumption of radial symmetry, a
quantum operator proportional to $1/r^2$ represents the cosmological constant
$\Lambda$. The experimentally measured value of $\Lambda$ is one of the
eigenvalues of $1/r^2$. Next we solve the Poisson equation $\nabla^2U=\Lambda$
for the gravitational potential $U(r)$, with the cosmological constant
$\Lambda(r)=1/r^2$ playing the role of a source term. It turns out that $U(r)$
includes, besides the standard Newtonian potential $1/r$, a correction term
proportional to $\ln r$ identical to that appearing in theories of modified
Newtonian dynamics.
