量子力學題解

前言

Quantum mechanics is an endless source of new questions and fascinating observations. Examples can be found in fundamental physics and in applied physics, in mathematical questions as well as in the currently popular debates on the interpretation of quantum mechanics and its philosophical implications.Teaching quantum mechanics relies mostly on theoretical courses, which are illustrated by simple exercises often of a mathematical character. Reduc- ing quantum physics to this type of problem is somewhat frustrating since very few, if any, experimental quantities are available to compare the results with. For a long time, however, from the 1950s to the 1970s, the only alterna- tive to these basic exercises seemed to be restricted to questions originating from atomic and nuclear physics, which were transformed into exactly soluble problems and related to known higher transcendental functions.In the past ten or twenty years, things have changed radically. The devel- opment of high technologies is a good example. The one-dimensional square- well potential used to be a rather academic exercise for beginners. The emer- gence of quantum dots and quantum wells in semiconductor technologies has changed things radically. Optronics and the associated developments in infra- red semiconductor and laser technologies have considerably elevated the social rank of the square-well model. As a consequence, more and more emphasis is given to the physical aspects of the phenomena rather than to analytical or computational considerations.Many fundamental questions raised since the very beginnings of quantum theory have received experimental answers in recent years. A good example is the neutron interference experiments of the 1980s, which gave experimental answers to 50 year old questions related to the measurability of the phase of the wave function. Perhaps the most fundamental example is the experimen- tal proof of the violation of Bell's inequality, and the properties of entangled states, which have been established in decisive experiments since the late 1970s, More recently, the experiments carried out to quantitatively verify de- coherence effects and "SchrSdinger-cat" situations have raised considerable.

內容概要

　　《量子力學題解：量子理論在現在物理中的應用(第2版)》方式獨特地展示了量子力學基本原理在原子分子物理、凝聚態(tài)物理、光學、量子信息和量子計算等學科中的應用。書中習題與現代量子力學實驗和理論聯系密切，部分題目有一定難度，可以深化讀者對物理概念的理解，為從事更深入的科學研究打下堅實的基礎。

作者簡介

作者：(法國) 比斯德溫特 (Basdevant.J.)

書籍目錄

Summary of Quantum Mechanics1 Principles2 General Results3 The Particular Case of a Point-Like Particle; Wave Mechanics.4 Angular Momentum and Spin5 Exactly Soluble Problems6 Approximation Methods7 Identical Particles8 Time-Evolution of Systems9 Collision ProcessesPart I Elementary Particles, Nuclei and AtomsNeutrino Oscillations1.1 Mechanism of the Oscillations; Reactor Neutrinos1.2 Oscillations of Three Species; Atmospheric Neutrinos1.3 Solutions1.4 Comments2 Atomic Clocks2.1 The Hyperfine Splitting of the Ground State2.2 The Atomic Fountain2.3 The GPS System2.4 The Drift of Fundamental Constants2.5 Solutions3 Neutron Interferometry3.1 Neutron Interferences3.2 The Gravitational Effect3.3 Rotating a Spin 1/2 by 360 Degrees3.4 Solutions4 Spectroscopic Measurement on a Neutron Beam4.1 Ramsey Fringes4.2 Solutions5 Analysis of a Stern-Gerlach Experiment5.1 Preparation of the Neutron Beam5.2 Spin State of the Neutrons5.3 The Stern-Gerlach Experiment5.4 Solutions6 Measuring the Electron Magnetic Moment Anomaly6.1 Spin and Momentum Precession of an Electron in a Magnetic Field6.2 Solutions Decay of a Tritium Atom7.1 The Energy Balance in Tritium Decay7.2 Solutions7.3 Comments The Spectrum of Positronium8.1 Positronium Orbital States8.2 Hyperfine Splitting8.3 Zeeman Effect in the Ground State8.4 Decay of Positronium8.5 SolutionsThe Hydrogen Atom in Crossed Fields9.1 The Hydrogen Atom in Crossed Electric and Magnetic Fields 9.2 Pauli's Result9.3 Solutions10 Energy Loss of Ions in Matter10.1 Energy Absorbed by One Atom10.2 Energy Loss in Matter10.3 Solutions10.4 CommentsPart II Quantum Entanglement and Measurement11 The EPR Problem and Bell's Inequality11.1 The Electron Spin11.2 Correlations Between the Two Spins11.3 Correlations in the Singlet State11.4 A Simple Hidden Variable Model11.5 Bell's Theorem and Experimental Results11.6 Solutions12 Schrodinger's Cat12.1 The Quasi-Classical States of a Harmonic Oscillator12.2 Construction of a Schr5dinger-Cat State12.3 Quantum Superposition Versus Statistical Mixture12.4 The Fragility of a Quantum Superposition12.5 Solutions12.6 Comments13 Quantum Cryptography13.1 Preliminaries13.2 Correlated Pairs of Spins13.3 The Quantum Cryptography Procedure13.4 Solutions14 Direct Observation of Field Quantization14.1 Quantization of a Mode of the Electromagnetic Field 14.2 The Coupling of the Field with an Atom14.3 Interaction of the Atom with an "Empty" Cavity14.4 Interaction of an Atom with a Quasi-Classical State14.5 Large Numbers of Photons: Damping and Revivals14.6 Solutions14.7 Comments15 Ideal Quantum Measurement15.1 Preliminaries: a yon Neumann Detector15.2 Phase States of the Harmonic Oscillator15.3 The Interaction between the System and the Detector15.4 An "Ideal" Measurement15.5 Solutions15.6 Comments16 The Quantum Eraser16.1 Magnetic Resonance16.2 Ramsey Fringes16.3 Detection of the Neutron Spin State16.4 A Quantum Eraser16.5 Solutions16.6 Comments17 A Quantum Thermometer17.1 The Penning Trap in Classical Mechanics17.2 The Penning Trap in Quantum Mechanics17.3 Coupling of the Cyclotron and Axial Motions17.4 A Quantum Thermometer17.5 SolutionsPart III Complex Systems18 Exact Results for the Three-Body Problem18.1 The Two-Body Problem18.2 The Variational Method18.3 Relating the Three-Body and Two-Body Sectors18.4 The Three-Body Harmonic Oscillator18.5 From Mesons to Baryons in the Quark Model18.6 Solutions19 Properties of a Bose-Einstein Condensate19.1 Particle in a Harmonic Trap19.2 Interactions Between Two Confined Particles19.3 Energy of a Bose-Einstein Condensate19.4 Condensates with Repulsive Interactions19.5 Condensates with Attractive Interactions19.6 Solutions19.7 Comments20 Magnetic Excitons20.1 The Molecule CsFeBra20.2 Spin-Spin Interactions in a Chain of Molecules20.3 Energy Levels of the Chain20.4 Vibrations of the Chain: Excitons20.5 Solutions

章節(jié)摘錄

插圖：The Ecole Polytechnique, one of France's top academic institutions, has a longstand- ing tradition of producing exceptional scientific textbooks for its students. The origi- nal lecture notes, the Cours de l'Ecole Polytechnique, which were written by Cauchy and Jordan in the nineteenth century, are considered to be landmarks in the develop- ment of mathematics.The present series of textbooks is remarkable in that the texts incorporate the most recent scientific advances in courses designed to provide undergraduate students with the foundations of a scientific discipline. An outstanding level of quality is achieved in each of the seven scientific fields taught at the Ecole: pure and applied mathe- matics, mechanics, physics, chemistry, biology, and economics. The uniform level of excellence is the result of the unique selection of academic staff there which in- cludes, in addition to the best researchers in its own renowned laboratories, a large number of world-famous scientists, appointed as part-time professors or associate professors, who work in the most advanced research centers France has in each field.Another distinctive characteristic of these courses is their overall consistency; each course makes appropriate use of relevant concepts introduced in the other textbooks. This is because each student at the Ecole Polytechnique has to acquire basic knowl- edge in the seven scientific fields taught there, so a substantial link between depart- ments is necessary. The distribution of these courses used to be restricted to the 900 students at the Ecole. Some years ago we were very successful in making these courses available to a larger French-reading audience. We now build on this success by making these textbooks also available in English.

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