Charge radius are used to determine the recommended values. The 2014 CODATA recommended values are: Recent measurement of the Lamb shift in muonic hydrogen (an exotic atom consisting of a proton and a negative muon) indicates a significantly lower value for the proton charge radius, : the reason for this discrepancy is not clear. Charge radius The rms charge radius is a measure of the size of an atomic nucleus, particularly of a proton or a deuteron. It can be measured by the scattering of electrons by the nucleus and also inferred from the effects of finite nuclear size on electron energy
Particle in a box which is proportional to formula_44. The variance in the position is a measure of the uncertainty in position of the particle: The probability density for finding a particle with a given momentum is derived from the wavefunction as formula_46. As with position, the probability density for finding the particle at a given momentum depends upon its state, and is given by where, again, formula_33. The expectation value for the momentum is then calculated to be zero, and the variance in the momentum is calculated to be: The uncertainties in position and momentum (formula_50 and formula_51) are defined as being equal