理論原子物理學

前言

The one and a half decades since the publication of the first edition of Theo-retical Atomic Physics have seen a continuation of remarkable and dramatic experimental breakthroughs. With the help of ultrashort laser pulses, special states of atoms and molecules can now be prepared and their time-evolution studied on time scales shorter than femtoseconds. Trapped atoms and mole-cules can be cooled to temperatures on the order of a few nano-Kelvin and light fields can be used to guide and manipulate atoms, for example in optical lattices formed as standing waves by counterpropagating laser beams. After the first production of Bose-Einstein condensates of ultracold atomic gases in 1995, degenerate quantum gases of ultracold atoms and molecules are now prepared and studied routinely in many laboratories around the world. Such progress in atomic physics has been well received and appreciated in the gen-eral academic community and was rewarded with two recent Nobel Prizes for physics. The 1997 prize was given to Steven Chu, Claude Cohen-Tannoudji and William Phillips for their work on cooling atoms, and only four years later Eric Cornell, Wolfgang Ketterle and Carl Wieman received the 2001 prize for the realization of the Bose-Einstein condensates mentioned above.The prominence of modern experimental atomic physics establishes fur-ther need for a deeper understanding of the underlying theory. The continuing growth in quality and quantity of available computer power has substantially increased the effectivity of large-scale numerical studies in all fields, including atomic physics. This makes it possible to obtain some standard results such as the properties of low-lying states in many-electron atoms with good accuracy using generally applicable programme packages. However, largely due to the dominant influence of long-ranged Coulomb forces, atomic systems are rather special. They can reveal a wide range of interesting phenomena in very differ-ent regimes——from near-classical states of highly excited atoms, where effects of nonlinearity and chaos are important, to the extreme quantum regime of ultracold atoms, where counterintuitive nonclassical effects can be observed. The theoretical solution of typical problems in modern atomic physics requires proficiency in the practical application of quantum mechanics at an advanced level, and a good understanding of the links to classical mechanics is almost always helpful. The aim of Theoretical Atomic Physics remains to provide the reader with a solid foundation of this sort of advanced quantum mechanics.In preparing the third edition I have again tried to do justice to the rapid development of the field. I have included references to important new work whenever this seemed appropriate and easy to do. Chapter I now includes a section on processes involving （wave packets of） continuum states and also an expanded treatment of the semiclassical approximation. Chapter 3 begins with a section illuminating the characteristic differences in the near-threshold properties of long-ranged and shorter-ranged potentials, and the first section of Chap. 4 contains a more elaborate discussion of scattering lengths. As a further "special topic" in Chap. 5 there is a section describing some aspects of atom optics, including discusions of the interactions of atoms with material surfaces and with light fields. The appendix on special mathematical functions has been slightly expanded to accommodate a few results that I repeatedly found to be useful.

內容概要

　　《理論原子物理學（第3版）》主要講解量子力學基本原理在現(xiàn)代原子物理學中的應用。在新版中，作者增添了理論原子物理領域的最新進展，介紹了目前大家非常感興趣的議題，包括半經典周期軌道理論、外場中原子的標度性質、雙電子原子的經典和量子動力學以及原子氣體的玻色－愛因斯坦凝聚等?！独碚撛游锢韺W（第3版）》還簡明介紹了原子光學中若干前沿研究，這是目前和未來超冷原子實驗必不可少的知識。作者強調基本理論的解釋，使讀者能夠理解標準理論結構里蘊藏的豐富物理思想，從而可以獨立進行科學研究工作。此外，形式各異的習題及其完整的解答過程為《理論原子物理學（第3版）》添色不少。《理論原子物理學（第3版）》被選為德國Springer出版社的“高等物理學教材”，這是一套非常優(yōu)秀的教材。目次：量子力學概要；原子和離子；原子光譜；簡單反應；專題；附錄：特殊數(shù)學函數(shù)；習題答案；索引?！　≡游锢硎俏锢韺W中最具有活力的前沿領域之一，它在推動人們對自然界的認知方面發(fā)揮了重要作用。在過去幾年里，該領域及相關領域因原子激光冷卻（1997年）、玻色-愛因斯坦凝聚的實現(xiàn)（2001年）以及光的量子相干性與精密光譜學的發(fā)展（2005年）三次摘取諾貝爾物理學獎桂冠。讀者對象：理論物理、原子分子物理和物理化學等專業(yè)的高年級本科生、研究生和相關領域的科研人員。

書籍目錄

1 Review of Quantum Mechanics1.1 Wave Functions and Equations of Motion1.1.1 States and Wave Functions1.1.2 Linear Operators and Observables1.1.3 The Harniltonian and Equations of Motion1.2 Symmetries1.2.1 Constants of Motion and Symmetries1.2.2 The Radial SchrSdinger Equation1.2.3 Example: The Radially Symmetric Harmonic Oscillator1.3 Bound States and Unbound States1.3.1 Bound States1.3.2 Unbound States1.3.3 Examples1.3.4 Normalization of Unbound States1.4 Processes Involving Unbound States1.4.1 Wave Packets1.4.2 Transmission and Reflection1.4.3 Time Delays and Space Shifts1.5 Resonances and Channels1.5.1 Channels1.5.2 Feshbach Resonances1.5.3 Potential Resonances1.6 Methods of Approximation1.6.1 Time-independent Perturbation Theory1.6.2 Ritz's Variational Method1.6.3 Semiclassical Approximation1.6.4 Inverse Power-Law Potentials1.7 Angular Momentum and Spin1.7.1 Addition of Angular Momenta1.7.2 Spin1.7.3 Spin-Orbit CouplingProblemsReferences2 Atoms and Ions2.1 One-Electron Systems2.1.1 The Hydrogen Atom2.1.2 Hydrogenic Ions2.1.3 The Dirac Equation2.1.4 Relativistic Corrections to the Schrodinger Equation2.2 Many-Electron Systems2.2.1 The Hamiltonian2.2.2 Pauli Principle and Slater Determinants2.2.3 The Shell Structure of Atoms2.2.4 Classification of Atomic Levels2.3 The N-Electron Problem2.3.1 The Hartree-Fock Method2.3.2 Correlations and Configuration Interaction2.3.3 The Thomas-Fermi Model2.3.4 Density Functional Methods2.4 Electromagnetic Transitions2.4.1 Transitions in General, "Golden Rule"2.4.2 The Electromagnetic Field2.4.3 Interaction Between Atom and Field2.4.4 Emission and Absorption of Photons2.4.5 Selection Rules2.4.6 Oscillator Strengths, Sum RulesProblemsReferences3 Atomic Spectra3.1 Long-Ranged and Shorter-Ranged Potentials3.1.1 Very-Long-Ranged Potentials3.1.2 Shorter-Ranged Potentials3.1.3 The Transition From a Finite Number to Infinitely Many Bound States, Inverse-Square Tails3.1.4 Example: Truncated Dipole Series in the H- Ion3.2 One Electron in a Modified Coulomb Potential3.2.1 Rydberg Series, Quantum Defects3.2.2 Seaton's Theorem, One-Channel Quantum Defect. Theory3.2.3 Photoabsorption und Photoionization3.3 Coupled Channels3.3.1 Close-Coupling Equations3.3.2 Autoionizing Resonances3.3.3 Configuration Interaction, Interference of Resonances3.3.4 Perturbed Rydberg Series3.4 Multichannel Quantum Defect Theory （MQDT）3.4.1 Two Coupled Coulomb Channels3.4.2 The Lu-Fano Plot3.4.3 More Than Two Channels3.5 Atoms in External Fields3.5.1 Atoms in a Static, Homogeneous Electric Field3.5.2 Atoms in a Static, Homogeneous Magnetic Field3.5.3 Atoms in an Oscillating Electric FieldProblemsReferences4 Simple Reactions4.1 Elastic Scattering4.1.1 Elastic Scattering by a Shorter-Ranged Potential411.2 Mean Scattering Lengths4.1.3 Near-Threshold Feshbach Resonances4.1.4 Semiclassical Description of Elastic Scattering4.1.5 Elastic Scattering by a Pure Coulomb Potential4.1.6 Elastic Scattering by a Modified Coulomb Potential, DWBA4.1.7 Feshbach Projection. Optical Potential4.2 Spin and Polarization4.2.1 Consequences of Spin-Orbit Coupling4.2.2 Application to General Pure Spin States4.2.3 Application to Mixed Spin States4.3 Inelastic Scattering4.3.1 General Formulation4.3.2 Coupled Radial Equations4.3.3 Threshold Effects4.3.4 An Example4.4 Exit Channels with Two Unbound Electrons4.4.1 General Formulation4.4.2 Application to Electrons4.4.3 Example4.4.4 Threshold Behaviour of Ionization Cross SectionsProblemsReferences5 Special Topics5.1 Multiphoton Absorption5.1.1 Experimental Observations on Multiphoton Ionization5.1.2 Calculating Ionization Probabilities via Volkov States5.1.3 Calculating Ionization Probabilities via Floquet States5.2 Classical Trajectories and Wave Packets5.2.1 Phase Space Densities5.2.2 Coherent States5.2.3 Coherent Wave Packets in Real Systems5.3 Regular and Chaotic Dynamics in Atoms5.3.1 Chaos in Classical Mechanics5.3.2 Traces of Chaos in Quantum Mechanics5.3.3 Semiclassical Periodic Orbit Theory5.3.4 Scaling Properties for Atoms in External Fields5.3.5 Examples5.4 Bose-Einstein Condensation in Atomic Gases5.4.1 Quantum Statistics of Fermions and Bosons5.4.2 The Effect of Interactions in Bose-Einstein Condensates5.4.3 Realization of Bose-Einstein Condensation in Atomic Gases5.5 Some Aspects of Atom Optics5.5.1 Atom-Wall Interactions5.5.2 Evanescent-Wave Mirrors5.5.3 Quantum ReflectionProblemsReferencesA Special Mathematical FunctionsA.1 Legendre Polynomials, Spherical HarmonicsA.2 Laguerre PolynomialsA.3 Gamma FunctionA.4 Bessel FunctionsA.5 Whittaker Functions, Coulomb FunctionsReferencesSolutions to the ProblemsReferencesIndex

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