Nuclear magnetic resonance
Nuclear magnetic resonance is the phenomenon by which some atomic nuclei, when placed in a magnetic field, can absorb radio waves of certain frequencies. It has chemical applications in the form of NMR spectroscopy and medical applications in the form of MRI.
NMR relies on the Zeeman Effect. Outside of a magnetic field, the energy levels of particles are dependent on the principal quantum number; the others are degenerate (the same energy). In a magnetic field, however, the magnetic energy levels cease to be degenerate and can cause the atomic nucleus to undergo energy transitions. These transitions, even in an extremely large field, are small. The energy is in the range of radio frequency radiation. When the radio waves are applied, by means of a transceiver coil (in principle no different to radio transceivers responsible for radio transmissions) certain frequencies are absorbed.
Different atomic nuclei will absorb different frequencies based on the strength of the magnetic field around the nucleus. Primarily, this is the applied field, which can be up to 18 teslas. However, the electrons surrounding the nucleus are also magnetic, altering the strength of the local field and therefore the frequency of energy absorbed. This is known as the chemical environment; nuclei in different chemical environments will absorb radio waves at different frequencies. When converted into a spectrum, this technique is one of the most powerful analytical tools in terms of quickly and easily determining chemical geometry.
 Technical limitations
Unlike other analytical tools, NMR requires relatively large quantities of material. The use of radio coils also makes it prone to very high noise levels that are by-products of the electronics.
 NMR on homeopathy
NMR is most sensitively applied to the proton, and as such water can be studied via NMR and sometimes produces some interesting effects due to hydrogen bonding. Thus the hypothesis that homeopathy "works" via water memory, and more specifically, by hydrogen-bonded clusters of water can be tested with high-sensitivity NMR experiments. No differences have been found between homeopathic dilutions and normal water. In one study, the relaxation times of the water protons were measured and determined to be exactly the same in both homeopathic dilutions and control substances. In theory, there could have been a slight difference if the succussion process lead to more air being dissolved in the liquid (paramagnetic oxygen notably shortens relaxation times) but there is no plausible mechanism by which this would have a medicinal effect anyway. Another study looked at additional peaks observed in the solutions at high sensitivity. The conclusion was again negative as despite many new NMR signals appearing in the study, most were identified as artefacts, and the rest as known or unidentified impurities and none were found more frequently or specifically in the homeopathic remedies than in the controls. The identification of impurities in homeopathic dilutions is telling of the fact that despite there being no "active" ingredient, there are other impurities that must also be affected by the succussion process - therefore if water memory is real, there is a high chance that a 50C solution has actually remembered the wrong thing entirely.