Elementary quantum mechanics of the neutron with an electric dipole moment

The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified nonrelativistic description of these two phenomena, in which the dipole moment operator, [Formula: see text], is not constrained to lie along the spin operator. Although the expectation value of [Formula: see text] in the neutron is less than [Formula: see text] of the neutron radius, [Formula: see text], the expectation value of [Formula: see text] is of order [Formula: see text] We determine the spin motion in external electric and magnetic fields, as used in past and future searches for a permanent dipole moment, and show that the neutron electric polarizability, although entering the neutron energy in an external electric field, does not affect the spin motion. In a simple nonrelativistic model we show that the expectation value of the permanent dipole is, to lowest order, proportional to the product of the time-reversal-violating coupling strength and the electric polarizability of the neutron.