Charge conservation elementary charge on positive and negative particles must be extremely close to equal, differing by no more than a factor of 10 for the case of protons and electrons. Ordinary matter contains equal numbers of positive and negative particles, protons and electrons, in enormous quantities. If the elementary charge on the electron and proton were even slightly different, all matter would have a large electric charge and would be mutually repulsive. The best experimental tests of electric charge conservation are searches for particle decays that would be allowed if electric charge is not always conserved. No such decays have ever
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