  We propose to test the electric neutrality of neutrons by a new technique
using the spectroscopy of quantum states of ultra-cold neutrons in the gravity
potential above a vertical mirror. The new technique is an application of
Ramsey's method of separated oscillating fields to neutron's quantum states in
the gravity potential of the earth. In the presence of an electric field E
parallel or antiparallel to the direction of the acceleration of the earth g,
the energy of the quantum states changes due to an additional electrostatic
potential if a neutron carries a non-vanishing charge. In the long run our new
method has the potential to improve the current limit for the electric charge
of the neutron by 2 orders of magnitude.
