Wave–particle duality operation of chemical reactions. Electricity, first thought to be a fluid, was now understood to consist of particles called electrons. This was first demonstrated by J. J. Thomson in 1897 when, using a cathode ray tube, he found that an electrical charge would travel across a vacuum. Since the vacuum offered no medium for an electric fluid to travel, this discovery could only be explained via a particle carrying a negative charge and moving through the vacuum. This electron flew in the face of classical electrodynamics, which had successfully treated electricity as a fluid for many years (leading to the
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