Jean-Louis Basdevant

• PhD
• Professor Emeritus at École Polytechnique

Ancient thinkers and builders were attracted by the optimality of phenomena and their applications. Archimedes studied the optimal form to be given to the hulls of ships, Aristotle, in a more metaphysical mind, claimed that the orbits of planets are circles because their even curvature, which shows neither an origin nor an end, must emanate from a...

Albert Einstein’s (1879–1955) masterpiece,Einstein, A. general relativity General relativityis based on the observation that two physical quantities that have a priori no relationship, are equal (or strictly proportional). This is, as we know, the two meanings of the concept of mass.

In itself, field theory is a vast domain that acquires its completeness when one considers the quantization of fields and the theory of fundamental interactions. We cannot ignore the practical importance of this subject in many present technologies, which range from the acoustics of concert halls to the many modes of communication, whether terrestr...

It is in the silence of laws that great actions are born.

William Rowland Hamilton (1805–1865) played a leading role in theoretical physics and mathematics in the 19th century—he was famous, among other things, for his discovery of quaternions on October 16, 1843, which he inscribed on the Broome bridge in Dublin with the formulas i2=j2=k2=ijk=-1. Born in Dublin, a child prodigy, he knew thirteen language...

Even a blind man could see what the god meant.

The variational principles present natural phenomena as processes Optimization under constraintsof optimization. The first example concerns the propagation of light rays between several mirrors, as observed by Hero of Alexandria, in the first century, who explained his experimental observations through geometric reasoning: in its way between severa...

The fundamental concepts and principles of mechanics, or dynamics, were established in the 17th century. Copernicus (1473–1543) gave the notion of reference system in 1543, and Galileo, G.Galileo (1564–1642) stated the principle of inertia in 1638 in his important work Discorsi e dimostrazioni mathematiche intorno a due nove scienze alla meccanica...

Richard Feynman (1918–1988) is probably the most brilliant theoretical physicist of the second half of 20th century. In his work at Princeton under the direction of John Archibald Wheeler, Feynman sought to solve the problem of divergent expressions in quantum field theory, which, together with Julian Schwinger and Sin-Itiro Tomonaga, was the reaso...

The explanation of spectroscopic data was one of the first great victories of quantum theory. In modern science and technology, the mastery of atomic physics is responsible for decisive progress ranging from laser technology to the exploration of the cosmos.

We explain the many experimental confirmations and properties of the “entangled states”, i.e. transmission of a quantum effect at a distance, and the number of applications that have transformed the intellectual thoughts of Einstein and John Bell in an industrial and fruitful “second quantum revolution” bearing many hopes, but leaving us with quest...

Quantum mechanics was born during the miraculous decade at the turn of the 20th century, when Röntgen’s 1895 discovery of X-rays in the Crookes tube sparked public enthusiasm, and where the following unexpected discoveries that have been made that have transformed the way we see the universe. In 1896, by reading Röntgen’s paper, Poincaré and Becque...

Quantum mechanics is inescapable. All physics is quantum physics, from elementary particles to the big bang, semiconductors, and solar energy cells. It is undoubtedly one of the greatest intellectual achievements of the history of mankind, probably the greatest of those that will remain from the 20th century. We describe here the major ideas and ex...

In quantum mechanics the number of problems for which there exist analytical solutions is rather restricted and one must resort to numerical results. In general one must also resort to approximation methods which are quite useful in order to understand such results. We present two of these methods: perturbation theory and the variational method. We...

During the years 1925–1927, quantum mechanics took shape and accumulated successes. Three persons, and not the least, addressed the question of its mathematical structure. In Zürich there was Erwin Schrödinger, in Göttingen David Hilbert, and in Cambridge Paul Adrien Maurice Dirac. This led to the present formulation of the theory.

The depth, the intellectual upheaval, and the philosophical implications of the Pauli principle are considerable. If this principle did not provoke the same interest as relativity among philosophers, and even among physicists, it is probably because it explained so many experimental facts (many more than relativity) that Fermi and Dirac incorporate...

When atomic spectral lines are observed with sufficient resolution, they appear to have in general a complex structure, each line being in fact a group of nearby components. This observation gives an explanation of fundamental interaction, as well as a major role in high technologies with atomic clocks, and allows an investigation of the cosmos.

We examine the question of physical quantities and their measurement. There are two questions; first, what does one find by measuring a physical quantity on a system whose state is known? The second is: what is a measurement process, what do we learn? These questions turn out to be difficult.

Here we adress a question which is often absent in similar books: what is the physical nature of the photon, is it a wave or a particle, how do these two features of light manifest themselves, and how do we manage with this concept which was at the center of most discussions in the elaboration of quantum mechanics? We cannot pursue the analysis com...

Spin 1/2 is the first truly revolutionary discovery of quantum mechanics. The properties of this physical quantity in itself, the importance of its existence, and the universality of its physical effects were totally unexpected.

Any experimental observation or any practical use of quantum phenomena relies on processes where a system evolves from a know initial state, and one performs measurements on it at some later time. In this Chapter we present some characteristic processes.

We explain the famous EPR arguments of 1935, and many of the reactions in the scientific world, including Schrödinger’s, who invented, in his answer the expression “entangled states”, since the EPR argument concerned two or more quantum states concerned with a global conservation law (Energy, momentum, angular momentum). David Bohm imagined a simpl...

The rotations of systems play a fundamental role in physics, be it in atomic spectra, in magnetic resonance imaging as well as in the stabilization of space crafts. The conservation laws of angular momentum play a central role, as important as energy conservation. The full results were proven as soon as 1913 by Elie Cartan in his classification of...

Going to polar coordinates gives: f(ρ)=(1/σ2)ρe-ρ2/2σ2(ρ≥0). One can check that ∫0+∞f(ρ)dρ=1.

We now study quantum mechanical problems in order to see how the theory works. We will consider the motion of particles in simple potentials and the quantization of energy. We will discover the tunnel effect, a most important quantum effect that leads us to modern applications and nanotechnologies.

In the previous Chapter, we described an interference experiment of atoms which, as we have understood, is both a wave and a probabilistic phenomenon. We now want to construct the theory of this experiment. More generally, we want to find the quantum theory of the simplest problem of mechanics; the nonrelativistic motion of a particle of mass m in...

Our axioms may be very elegant and profound, but they seem to be deprived of substance. Within this framework, how does one treat a particular case? What are the Hamiltonian and the observables for a given system? In wave mechanics, we have operators p^x=-iħ(∂/∂x), H^=p2/2m+V and we solve differential equations, but what should we do here? It is tr...

In the previous chapter, we saw how Heisenberg’s matrix mechanics arose in 1924–1925. What we want to do here is consider the problem of the NH3 molecule with the method seen in Chap. 5 and to do matrix mechanics on this particular case, in a similar way to what we did in wave mechanics by considering the simple problem of the motion of a particle...

We show how quantum mechanics can provide a procedure to send safely a message to a correspondent and to minimize the risk for this message to be intercepted by an unwanted outsider.

We show that superpositions of macroscopic states, such as the “Schrödinger cat” which is in a superposition of the “dead” and “alive” states, are not detectable in practice. They are extremely fragile, and a very weak coupling to the environment suffices to destroy the quantum superposition of the two states.

The ground state of the external electron of an alkali atom such as rubidium and cesium is split by the hyperfine interaction between the electron magnetic moment and the nuclear magnetic moment. We show in this chapter how one can use this hyperfine splitting to devise atomic clocks of high accuracy.

We evaluate the energy loss of a charged particle in matter, by studying the modifications that the state of an atom undergoes when the charged particle passes in its vicinity. This process can be used to identify the products of a nuclear reaction.

In the following pages we recall the basic definitions, notations and results of quantum mechanics.

We study quantum boxes (also called quantum dots) of nanometric dimensions, inside which the conduction electrons of a solid are confined at low temperatures. The possibility to control the energy levels of such devices leads to very interesting applications in micro-electronics and opto-electronics.

In the Dirac equation, the gyromagnetic factor g of the electron is equal to 2. In quantum field theory, one predicts a value of g slightly different from 2. The purpose of this chapter is to study the measurement of the quantity g − 2.

The positronium is a neutral atomic system consisting of an e⁺e⁻ pair, where the positron e⁺ is the antiparticle of the electron. Here we study the energy levels of this system, in particular the hyperfine splitting of its ground state. We also investigate the decay of positronium due e⁺ − e⁻ annihilation.

We study a practical example of what von Neuman defined as an ideal quantum measurement. It consists in measuring the excitation number of a harmonic oscillator by the phase of another oscillator coupled to it.

We consider the dynamics of a two-level atom interacting with a single mode of the quantized electromagnetic field. We show that specific features occur, such as damping and revivals of the Rabi oscillations of the atom.

The rotation of a quantum fluid, a Bose–Einstein condensate for instance, is very different from that of a classical gas. In this chapter, we study the mechanism that leads to the formation of one or several quantized vortices in the rotating gas.

We consider an electron confined in a Penning trap and coupled to the thermal radiation. We investigate the quantum transitions of the system between various energy levels, and show that their rate provide a determination of the temperature.

We study a simple version of the motion of a particle in a one-dimensional chain of regularly spaced sites. We encounter the surprising phenomenon of Bloch oscillation: when one adds a constant force to the one created by the periodic lattice, the particle oscillates in space, which is very different from the motion that occurs in the absence of th...

We derive rigorous lower bounds on three-body ground state energies. Upper bounds are easier to obtain by variational calculations. These lower bounds are quite close to the exact answers, to which they provide useful approximations.

We analyze a Stern–Gerlach experiment from both a practical and a conceptual point of view. The experiment is performed on a monochromatic beam of neutrons crossing a region of strongly inhomogeneous magnetic field.

In a quantum process where the superposition of two probability amplitudes leads to an interference phenomenon, we first show that the interferences disappear if an intermediate measurement gives information about which path has actually been followed. Next, we show that the interferences reappear if this information is “erased” by a quantum device...

Flavor neutrinos νe, νμ and ντ, which are produced or detected experimentally, do not have definite masses. Therefore, a neutrino with a given flavor transforms spontaneously and periodically into neutrinos with different flavors. In this chapter, we explore how this oscillation, combined with the interaction of neutrinos with matter in the Sun, mo...

Some pigments are made of linear molecular ions, along which electrons move freely. We derive here the energy levels of such an electronic system and we show how this energy scheme explains the observed color of the pigments.

We study the magnetic excitations of a long chain of coupled spins. We show that one can associate the excited states of the system with quasi-particles that propagate along the chain.

We present a very precise method due to Norman Ramsey for spectroscopic measurements. We analyse it in the case of a neutron beam, where it can be used to determine the neutron magnetic moment.

We study the reflection of very slow hydrogen atoms from the surface of a liquid helium bath. Sticking of an atom on the bath may occur via the excitation of a surface wave, called a ripplon. We show that this probability vanishes at low temperatures, which can ultimately lead to a specular reflection of the atoms on the surface.

We study the modification of the energy spectrum of a hydrogen atom placed in crossed static electric and magnetic fields, and we recover a result first derived by Wolfgang Pauli.

We study an interferometric method allowing one to determine if a given bomb is real or factitious without exploding it. We present first a two-path interferometric setup which has a relatively low merit factor. Then we analyze a multiple-wave interference scheme, which can have an arbitrarily good detection efficiency.

We study two interference experiments performed with neutrons which prove the influence on the interference pattern of (i) the gravitational field and (ii) a 2π rotation of the neutron spin.

We describe a very efficient technique for probing the structure of crystals. It consists in forming, inside the material, pseudo hydrogenic atoms made of an electron and a positive muon, called muonium.

By shining laser light onto an assembly of neutral atoms or ions, it is possible to cool and trap these particles. We study a simple cooling mechanism, Doppler cooling, and we derive the corresponding equilibrium temperature. Then, we show that the cooled atoms can be confined in the potential well created by a focused laser beam.

We study specific properties of quantum mechanics, whose paradoxical character has been pointed out by Einstein, Podolsky and Rosen. We consider the example of entangled states for the spins of two particles, and the famous theorem of John Bell whose experimental test is definitely in favor of quantum mechanics.

Many molecular species, such as free radicals, possess an unpaired electron. We show in this chapter how the magnetic spin resonance of this electron, called electron spin resonance (ESR), can provide useful information about the structure of the molecule.

We study a Bose–Einstein condensate, i.e. the ground state of a weakly interacting N-boson system, confined in a harmonic potential. The interactions between particles may be repulsive or attractive and are taken into account at the mean-field level.

We study diffraction phenomena which reveal the existence of the dimer He2 and the trimer He3. Turning to the case of larger objects, we set a bound on the maximal size of molecules that can be studied by diffraction or interference effects.

We consider in this chapter correlated states involving more than two particles. We show that the violation of Bell’s inequality that is known for a two-particle system (see Chap. 10.1007/978-3-030-13724-3_11) is then replaced by an even more spectacular contradiction.

Augustin Fresnel was born in 1788, in the Normandy village of Broglie where his father was employed as an architect by the duc de Broglie. The author of the wave theory of light was thus born on lands that would later belong to Louis de Broglie, the author of the wave theory of matter, whose birth came a century later. Fresnel’s work was accomplish...

This textbook presents problems with detailed solutions showing how to apply quantum theory to modern physics. The text is divided in three parts, the first dealing with elementary particles, nuclei and atoms, the second presents quantum entanglement and measurement. Finally complex systems are examinated in depth. The aim of the text is to guide t...

The Lorentz force acting on a particle of charge q moving with a velocity v in a magnetic field B, does not derive from a potential. Therefore, the formulation of quantum mechanics we have used up to now does not apply.

Physics is a fascinating adventure between the eye and the mind, between the world of phenomena and the world of ideas. Physicists look at Nature and ask questions to which they try and imagine answers. And the interplay, often the quarrel, between what we observe and what we construct “logically” is always a source of amazement. A discovery is oft...

Our axioms may be very elegant and profound, but they seem to be deprived of substance. Within this framework, how does one treat a particular case? What are the Hamiltonian and the observables for a given system? In wave mechanics, we have operators \(\hat{p}_x=-i\hbar (\partial /\partial x)\), \(\hat{H} =p^2/2m+V\) and we solve differential equat...

The rotations of systems play a fundamental role in physics, be it in atomic spectra, in magnetic resonance imaging as well as in the stabilization of space crafts. The conservation laws of angular momentum play a central role, as important as energy conservation. We make use of this fact when we study the hydrogen atom.

Spin 1/2 is the first truly revolutionary discovery of quantum mechanics. The properties of this physical quantity in itself, the importance of its existence, and the universality of its physical effects were totally unexpected.

During the years 1925–1927, quantum mechanics took shape and accumulated successes. But three persons, and not the least, addressed the question of its structure. In Zürich there was Erwin Schrödinger, in Göttingen David Hilbert, and in Cambridge Paul Adrien Maurice Dirac.

In the previous chapter, we saw how Heisenberg’s matrix mechanics arose in 1924–1925. What we want to do here is to come back to the problem of the NH\(_3\) molecule, seen in Chap. 5 and to do matrix mechanics on this particular case, in a similar way to what we did in wave mechanics by considering the simple problem of the motion of a particle in...

The depth, the intellectual upheaval, and the philosophical implications of the Pauli principle are considerable. If this principle did not provoke the same interest as relativity among philosophers, and even among physicists, it is probably because it explained so many experimental facts (many more than relativity) that Fermi and Dirac had incorpo...

Here we are dealing with a difficult subject. Things are far from obvious, but their manipulation is simple and they become quickly familiar when one manipulates the theory. We really face the problem that the relation between physical concepts and their mathematical representation is not obvious in quantum mechanics.

At the end of Chap. 3 we mentioned Einstein’s revolt against the probabilistic aspect of quantum mechanics and the uncertainty relations. As we said, Einstein was worried about two aspects. One is the notion of a complete description of reality. He thought that a complete description is possible in principle, and that the probabilistic description...

In quantum mechanics the number of problems for which there exist analytical solutions is rather restricted. In general one must resort to approximation methods. In this chapter, we present two of these methods: perturbation theory and the variational method. We are mainly interested in applications.

The explanation of spectroscopic data was one of the first great victories of quantum theory. In modern science and technology, the mastery of atomic physics is responsible for decisive progress ranging from laser technology to the exploration of the cosmos.

Any experimental observation or any practical use of quantum phenomena relies on processes where a system evolves from a know initial state, and one performs measurements on it at some later time.

Quantum mechanics is inescapable. All physics is quantum physics, from elementary particles to the big bang, semiconductors, and solar energy cells. It is undoubtedly one of the greatest intellectual achievements of the history of 1mankind, probably the greatest of those that will remain from the 20th century, before psychoanalysis, computer scienc...

We now solve quantum mechanical problems in order to see how the theory works. We we consider the motion of particles in simple potentials and the quantization of energy.

When atomic spectral lines are observed with sufficient resolution, they appear to have in general a complex structure, each line being in fact a group of nearby components.

This chapter contains the solutions to the exercises proposed in the text.

In the first chapter, we described an interference experiment of atoms which, as we have understood, is both a wave and a probabilistic phenomenon.

The new edition of this remarkable text offers the reader a conceptually strong introduction to quantum mechanics, but goes beyond this to present a fascinating tour of modern theoretical physics. Beautifully illustrated and engagingly written, it starts with a brief overview of diverse topics across physics including nanotechnology, statistical ph...

We show that a single $I=1$ spin-parity $J^{PC}= 1^{++}$ $a_1$ resonance can manifest itself as two separated mass peaks, one decaying into an S-wave $\rho\pi$ system and the second decaying into a P-wave $f_0(980)\pi$ system, with a rapid increase of the phase difference between their amplitudes arising mainly from the structure of the diffractive...

The high statistics COMPASS results on diffractive dissociation $\pi N \rightarrow \pi \pi \pi N$ suggest that the isospin $I=1$ spin-parity $J^{PC}= 1^{++}$ $a_1(1260)$ resonance could be split into two states: $a_1(1260)$ decaying into an S-wave $\rho\pi$ system, and $a_1^\prime(1420)$ decaying into a P-wave $f_0(980)\pi$ system. We analyse the r...

he hallmark of a good book of problems is that it allows you to become acquainted with an unfamiliar topic quickly and efficiently. The Quantum Mechanics Solver fits this description admirably. The book contains 27 problems based mainly on recent experimental developments, including neutrino oscillations, tests of Bell's inequality, Bose Einstein c...

At the end of chapter 3, we mentioned Einstein’s revolt against the probabilistic aspect of quantum mechanics and the uncertainty relations. As we said, Einstein was worried about two aspects. One is the notion of a complete description of reality. He thought that a complete description is possible in principle, and that the probabilistic descripti...

Optimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion of equilibrium was dear to thinkers of the enlightenment, as illustrated by Montesquieus famous formulation: "In all magistracies,...

Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the openin...