Classical mechanics uses Newton’s second law to determine the position of a particle at any given time. This can then be used to determine velocity, momentum, kinetic energy, or any other dynamical variable of interest. In contrast, quantum mechanics looks for the particle’s wave function, which it gets by solving the Schrödinger equation.
The wave function is spread out in space (as opposed to being localized at a point). How this can represent the state of a particle is explained by Born’s statistical interpretation, which gives only a probability for finding a particle at a given point. The statistical interpretation introduces a kind of indeterminacy into quantum mechanics – the outcome of an experiment to measure a particle’s position cannot be predicted with certainty but can give only statistical information about the possible results.
If a particle’s position was measured and determined to be at a certain point, there is the question of where the particle was just before the measurement was made. Experiments have confirmed the Copenhagen interpretation, which is that the particle doesn’t have a precise position prior to measurement. A repeated measurement performed immediately after the first must return the same value; the first measurement caused the wave function to collapse.
A spread in wavelength corresponds to a spread in momentum, therefore the more precisely a particle’s location is determined, the less precisely its momentum is determined. This is known as Heisenberg’s uncertainty principle.
—July 2020
Lance Jones 