You can read all sort of new age weirdness and academic pomposity associated with quantum mechanics. Controversy rages on up to this day about the fundamentals of this cornerstone of modern physics.
So what is so special about QM. My interest in it comes from the mathematical framework it was built on. I think it’s an interesting way to learn new mathematics, and indeed it has proven to be just that. My experience has been that once you finally get the hang of it, all the mystery you’ve read about it seems to diffuse in to thin air.
It is easy to deflate QM, if for some strange reason that is your goal. The basic premise the quantum is built on is diffusion. Yes, the Schrödinger wave equation is nothing more than a mathematical description of diffusion in imaginary time. All the nonintuitive aspects of QM are closely related to the complex plane. Schrödinger equation was an important step in the development of the theory, but is actually just a small part of the framework and it is incomplete without the concept of what a measurement is.
Of all the books written about QM I’ve studied, the best introduction by far is in the good old communist era Landau and Lifshitz book Course of Theoretical Physics Volume 3: Quantum Mechanics (Non-relativistic Theory). It gets right to the point; it is impossible to measure properties of fundamental particles with absolute precision. The reason is simple and intuitive. Measurements of fundamental particles have to be made with some sort of force mediating way. In the case of measuring the position of an electron you can use light. The more precision you want, the shorter wavelength you’ll end up using. This in turn means that the photon carries more energy. When the photons interact and scatter with the electron you want to measure, the more the electron recoils from this energy. Repeated measurements will end up jittering the particle more and more, adding to the uncertainty of the measured path. Consecutive lower energy, bigger wavelength photons end up jittering the particle’s path less, but the wavelength dictates the uncertainty in the measurement.
This ends up being reproduced by the basic QM vector space framework. The Heisenberg uncertainty principle in the mathematics stems from the commutation relations of the observables, which in the simplest case here are the position and momentum of the particle.
The above video illustrates the unitary time evolution and diffusion of a simple potential well quantum system in both the position and momentum spaces. The initial gaussian probability distribution moves and spreads out in space with time. The distribution cancels out with itself in this bound system, in free space the wave packet would diffuse indefinetly. You don’t actually exactly know where the particle is until you measure it, and collapse the wave function to some specific state. For example measuring the position would pick a definite position from the distribution at random with some probability and the time evolution would diffuse from that point on, until a new measument is made.
Is it then such a mystery that QM manages to be backed up by experimental measurements, when the whole theory is rigged up to do exactly that?