In classical mechanics, the mathematical equations discovered by Newton govern the positions and velocities of particles. But in quantum mechanics, the Schrödinger equation governs the motion of the wave functions. So it is the wave functions which are the ‘physical objects’ in the mathematics of quantum mechanics; particles never enter the mathematics.

A useful visual picture of the wave function is that it is matter spread out in a mist or cloud of varying density. The Schrödinger equation determines the shape and density of the cloud, and how it moves through space. If there are several ‘particles,’ the total wave function may be pictured as several separate (or sometimes overlapping) clouds, with the Schrödinger equation determining how the clouds interact. The wave function of a macroscopic object like a cat or a human being, composed of billions of ‘single particle’ individual wave functions, is extremely complicated, but that does not prevent us from deducing certain relevant general characteristics.

What is the wave function? At this point in time, we must think of it simply as ‘that which makes up matter.’ It cannot currently be described in terms of something else. (See, however, the last paragraph in Mass, Spin, Charge and the Wave Function)


We often have to refer to the ‘state’ of a particle or detector or observer—the location of a silver atom, a detector reading yes or no, an observer perceiving a live or dead cat. We will sometimes use square brackets, [label], and sometimes the ‘ket’ notation , where the label describes the relevant property—the position of a silver atom, whether a cat is alive or dead, the ‘spin’ of an electron, and so on—of the wave function.

Technically the ‘ket’ refers to the abstract ‘state vector’. But there is no easy visualization of the state vector, so, since the wave function contains all the necessary information, we will not use the term.

What is the relation of the wave function to the particles—electrons and so on—that presumably make up matter? In spite of the fact that we almost reflexively think of matter as made up of particles, we will show there is No Evidence for Particles; the wave function possesses all the properties necessary to explain our particle-like world. (Nevertheless, because the word ‘particle’ is so useful, we will continue to use it but one must remember it is just shorthand for certain properties of the wave function.)