Conceptual Quantum Mechanics

This is a textbook that provides a conceptual introduction to Quantum Mechanics, following a teaching approach quite different from the usual. Far from using excessively dense formalism, as is so often the case, the main ideas are still treated with mathematical precision, relying on a basic knowledge of Newton's laws, wave motion, and Calculus. It is addressed to all interested readers, or teachers, particularly including undergraduate students of any branch of science or engineering.

Quantum Mechanics is an utterly important discipline, increasingly integrated in our knowledge society, spanning all fields of technology. In this book Feynman's formulation is used to bridge the gap between mathematical precision and the use of intuitive classical reference points that every student has learned.

The implication of time in the precise definition of quantum fluctuations and of the Planck constant is analised first, portraying the main role these play in Nature, for both the motion of bodies of given mass m, and waves. Duality does not mean identifying particles with waves, but rather revealing what they have in common, namely the random character of their motion, and the non deterministic nature of measurements.

The Planck constant brings about the finite sizes of atoms and atomic nuclei, thus allowing for the storage of energy in the Universe. The properties of quanta (photons, phonons, gluons), are not just accidental, but constitute the basic root of Mechanics, to which they give name.

Schrödinger's equation is deduced, not postulated, as in most existing textbooks. The necessity of using complex numbers for the description of motion is also conceptually derived, as opposed to their non appearance in classical mechanics. The simplest and most suitable formalism turns out to be Feynman's, for it allows giving full meaning to the wave function, which is key for accurate understanding of angular momentum, spin, chemical bonds, magnetism, quantum tunneling, or entropy.

Being perhaps the most subtle concept of Quantum Mechanics, a specific discussion is made of the stationary states, which impregnate the different versions of the quantum formalism, starting out from their classical counterpart of periodic motion, both chaotic and non chaotic. The fundamental role of the quantum vacuum is also emphasized, which causes the immersion of Quantum Mechanics into the more perfect theory of quantum fields. The origin of the Pauli exclusion principle is established, as intimately connected with the electron spin, further illustrated with the most suggestive cases of bosonic and fermionic systems.

The book offers, in a brief and succint way (less than 190 pages, with 39 mathematical figures), the main ideas and key tools that will enable the student assessing and solving an infinite number of problems, covering quite different fields.