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I. The Formalism of Quantum Mechanics

I.1. The Wave-Particle Duality and the Emergence of Quantum Mechanics

Whatever your scientific background is, you probably know very well by now that light, like sound waves, is a wave. At the beginning of the 20th century, Albert Einstein showed that light must be composed of small particles, which he called photons (the first scientific argument that light was composed of actual particles was given in the 11th century by Ibn al-Haitham in Cairo.) Therefore, light is now considered to have what we call a wave-particle duality: it is both a wave, and is composed of small elementary particles―or “photons”.

In 1924, French physicist Louis de Broglie proposed, in what is possibly the most cited PhD thesis of all time, a hypothesis that all particles actually possess the same duality. That is, all particles have in fact wave properties, not just photons. This hypothesis was confirmed experimentally three years later.

With the beginning of the 20th century, physicists had realized that classical physics failed to explain several phenomena. A new physics was obviously needed. The first real step towards the new understanding of nature, upon which scientists would base their new theory, was the wave-particle duality.

This new theory which was called Quantum Mechanics. It was mainly developed in the 1920’s, by several scientists, most notably Erwin Schrödinger and Werner Heisenberg.

I.2. The Wave Function. The Formalism of Quantum Mechanics

Each particle has several properties, like mass, energy and position, for example. And the particle can have different values of each of these physical quantities. Again for example, a particle can weight 2 grams and be at a position x in space, or can weight 1 gram and be in a position x+3 in space. The ensemble of all the values of the particle’s properties is called a “state”. A “state” means very simply the condition in which the particle is in.

Now, since QM is based on the fact that particles possess wave properties, it associates what we call a “wave function” to each particle. To put this very simply, this function is a way to account for the particle’s wave properties. And since classical mechanics, which we are now looking to abandon, was based on the “particular” nature of the particle, QM is based on its wave-like nature. Therefore, physicists formulated the wave function as to be able to describe the whole state of the particle. In order for it to do so, this wave function must be a function of the particle’s position and it’s time (i.e. it depends on the position of the particle at a certain time. This is enough to know all the remaining properties of the particle!) We note this mathematical function ψ(r,t), where r is the position of the particle, and t is the time.

In the next article we will finally discuss the bizarre implications of QM and whether or not nature is actually non-deterministic.

References

* C. Aslangul, Cours Magistère de Physique, Université Paris VI, 2004

* J.L. Basdevant & J. Dalibard, Cours de l’École Polytechnique, 2002

* H. Young & R. Freedman, University Physics, 12th Ed.

* Wikipedia, ‘‘The Copenhagen Interpretation’’, retrieved 3/18/2022 from http://en.wikipedia.org/wiki/Copenhagen_interpretation