  NMR imaging without any radio-frequency magnetic field is explained by a
quantum treatment of independent spin~$\tfrac 12$. The total magnetization is
determined by means of their individual wave function. The theoretical
treatment, based on fundamental axioms of quantum mechanics and solving
explicitly the Schr\"{o}dinger equation with the kinetic energy part which
gives the motion of free spins, is recalled. It explains the phase shift of the
spin noise spectrum with its amplitude compared to the conventional NMR
spectrum. Moreover it explains also the relatively good signal to noise ratio
of NMR images obtained without a RF pulse. This derivation should be helpful
for new magnetic resonance imaging sequences or for developing quantum
computing by NMR.
