# Quantum, noncommutative and MOND corrections to the entropic law of gravitation. (arXiv:1709.04339v1 [physics.gen-ph])

Quantum and noncommutative corrections to the Newtonian law of inertia are

considered in the general setting of Verlinde's entropic force postulate. We

demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in

a classical setting by seeking appropriate corrections in the entropy.We

estimate the correction term by using concrete coherent states in the standard

and generalized versions of Heisenberg's uncertainty principle. Using Jackiw's

direct and analytic method we compute the explicit wavefunctions for these

states producing minimal length as well as minimal products. Subsequently we

derive a further selection criterion restricting the free parameters in the

model in providing a canonical formulation of the quantum corrected Newtonian

law by setting up the Lagrangian and Hamiltonian for the system.