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| 当前位置:首页->文学-> ->非相对论量子力学 第3版(理论物理学教程 第3卷) | |
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非相对论量子力学 第3版(理论物理学教程 第3卷)作者:EMLifshitz,LDLandau,分类:文学 人气: 装帧:平装 / 24开 / 677页 / 0字 ISBN(10位/13位):7506242575 出版:世界图书出版公司于1999-05- 1出版 定价:¥86元 标签(Tags): 收藏人数： |
| 简介: |
| 量子力学著作繁多，L.D.Landou的这本一向广受好评。该书内容丰富，但是数学基础不好，看起来会比较吃力。 |
| 目录: |
| CONTENTS From the Preface to the first English edition Preface to the second English edition Preface to the third Russian edition Editor'. Pretace to the Iburth Russian edition Notation 1. THE BASIC CONCEPTS OF QUANTUM MECHANICS 1. The uncertainty principlc 2. The principle of superposition 3. Operators 4. Addition and multiplication of operators 5. The continuous spectrum 6. The passage to the limiting case of classical mechanica 7. The wave function and measurements II. ENERGY AND MOMENTUM 1.The Hamiltonian operator 2. The differentiation of operators with respect to time 3. Stationary states 4. Matrices ?5. Transformation of matrices ?6. The Heisenberg representation of operators ?7. The density matrix ?8. Momentum ?9. Uncertainty relations III. SCHRODINGER'S EQUATION ?1 Schrodinger's equation ?2. The fundamental properties of Schrodinger's equation ?3. The current density ?4. The variational principle ?5. General properties of motion in one dimension ?6. The potential well ?7. The linear oscillator ?8. Motion in a homogeneous field ?9. The transmission coefficient IV. ANGULAR MOMENTUM ?1. Angular momentum ?2. Eigenvalues of the angular momcntum ?3. Eigenfunctions of the angular momentum 4.Matrix elements of vectors 5.Parity of a state 6.Addition of angular momenta V. MOTION IN A CENTRALLY SYMMETRIC FIELD 1.Motion in a centrally symmetric field 2.Spherical waves 3.Resolution of a plane wave Fall of a particle to the centre 4.Motion in a Coulomb field (spherical polar coordinates) 5.Motion in a Coulomb field (parabolic coordinates) VI. PERTURBATION THEORY Perturbations indcpendent of time The secular equation Perturbations depending on time Transitions under a perturbation acting for a finite time Transitions under the action of a periodic perturbation Transitions in the continuous spectrum The uncertainty relation for energy Potential energy as a perturbation VII. THE QUASI-CLASSICAL CASE The wave function in the quasi-classical case Boundary conditions in the quasi-classical case Bohr and Sommerfeld's quantization rule Quasi-classical motion in a centrally symmetric field Penetration through a potential barricr Calculation of the quasi-classical matrix elements The transition probability in the quasi-classical case Transitions under the action of adiabatic perturbations VIII SPIN Spin The spin operator Spinors The wave functions of particles with arbitrary spin The operator of finite rotations Partial polarization of particles Time reversal and Kramers' theorem IX. IDENTITY QF PARTICLES The principle of indistinguishability of similar particles Exchangc interaction ?3. Symmetry with respect to interchange ?4. Second quantization. The case of Bose statistics ?5. Second quantization. The case of Fermi statistics X THE ATOM ?6. Atomic energy levcls ?7. Electron states in the atom ?8. Hydrogcn-like cnergy levcls ?9. The self-consistent field ?0. The Thomas-Fermi equation ?1. Wave functions of the outer electrons ncar the nucleus ?2. Fine structurc of atomic lcvels ?3. The Mendeleev periodic system ?4. X-ray terms ?5. Multipole moments ?6. An atom in an electric field ?7. A hydrogen atom in an electric field XI THE DIATOMIC MOLECULE ?8. Electron terms in the diatomic molccule ?9. The intersection of electron terms ?0. The relation between molecular and atomic terms ?1. Valency ?2. Vibrational and rotational structurea of singlet terms in the diatomic molecule ?3. Multiplet terms. Casc a ?4. Multiplet tcrms. Case b ?5. Multiplet tcrms. Cases c and d ?6. Symmetry of molecular terms ?7. Matrix elements for the diatomic molecule ?8. A-doubling ?9. The interaction of atoms at large distances ?0. Pre-dissociation XII THE THEORY OF SYMMETRY ?1. Symmetry transformations ?2. Transformation groups ?3. Point groups ?4. Representations of groups ?5. Irreducible representations or point groups ?6. Irreducible representations and the classification of terms ?7. Selection rulcs for matrix elemcnts ?8. Continuous groups ?9. Two-valucd rcpresentations of finitc point groups XIII POLYATOMIC MOLECULES ?00. Thc classification of molecular vibrations ?01. Vibrational cncrgy levcls ?02. Stability of symmetrical configurations of the molecule ?03. Quantization of the rotation of a top ?04. The interaction between the vibrations and the rotation of the molecule ?05. Thc classification of molecular tenns XIV ADDITION OF ANGULAR MOMENTA ?06. 3j-symbols ?07. Matrix elements of tensors ?08. 6j-symbols ?09. Matrix elements for addition of angular momenta ?10. Matrix elements for axially symmetric systems XV MOTION IN A MAGNETIC FIELD ?11. Schrodinger's equation in a magnetic field ?12. Motion in a uniform magnetic field ?13. An atom in a magnetic field ?14. Spin in a variable magnetic field ?15. The current density in a magnetic field XVI NUCLEAR STRUCTURE ?16. Isotopic invariance ?17. Nuclear forces ?18. The shell model ?19. Non-spherical nuclei ?20. Isotopic shift ?21. Hyperfine structure of atomic levels ?22. Hyperfine structure of molecular levels XVII. ELASTIC COLLISIONS ?23. The general theory of scattering ?24. An investigation of the general formula ?25. The unitarity condition for scattering ?26. Bom's formula ?27. The quasi-classical case Analytical properties of the scattering amplitude The dispersion relation The scattering amplitude in the momentum representation Scattering at high energies The scattering of slow particles Resonance scattering at low energies Resonance at a quasi-discrete level Rutherford's formula The system of wave functions of the continuous spectrum Collisions of like particles Resonance scattering of charged particles Elastic collisions betvveen fast electrons and atoms Scattering with spin-orbit interaction Regge poles XVIII INELASTIC COLLISIONS Elastic scattering in the presence of inelastic processes Inelastic scattering of slow particles The scattering matrix in the presence of reactions Breit and Wigner's formulae Interaction in the final state in reactions Behaviour of cross-sections near the reaction threshold Inelas'tic collisions between fast electrons and atoms The effective retardation Inelastic collisions between heavy particles and atoms Scattering of neutrons Inelastic scattering at high energies MATHEMATICAL APPENDICES a. Hermite polynomials b. The Airy function c. Lcgcndre polynomials d. The confluent hypergcometric function e. The hypergcometric function f. The calculation of integrals containing confluent hypergcometric functions Index |
| 内容摘要: |
| THE BASIC CONCEPTS OF QUANTUM MECHANICS ? The uncertainty principle WHEN we attempt to apply classical mechanics and electrodynamics to explain atomic phenomena, they lead to results which are in obvious conflict with expcriment. This is very clearly seen from the contradiction obtained on applying ordinary electrodynamics to a model of an atom in which the elec- trons move round the nucleus in classical orbits. During such motion, as in any accelerated motion of charges, the electrons would have to emlt electro- magnetic waves continually. By this emission, the electrons would lose their energy, and this would eventually cause them to fall into the nucleus. Thus, according to classical electrodynamics, the atom would be unstable, which does not at all agree with reality. This marked contradiction between theory and experiment indicates that the construction of a theory applicable to atomic phenomena-that is, pheno- mena oocurring in particles of very small mass at very small distances- demands a fundamental modification of the basic physical concepts and laws. As a starting-point for an investigation of these modifications, it is conveni- ent to take the experimentally observed phenomenon known as electron diffraction. It is found that, when a homogeneous beam ofelectrons passes through a crystal, the emergent beam exhibits a pattern of alternate maxima and minima of intensity, wholly similar to the diffraction pattern observed in the diffraction of electromagnetic waves. Thus, under certain conditions, the behaviour of material particles-in this case, the electrons-displays features belonging to wave processes. How markedly this phenomenon contradicts the usual ideas of motion is best seen from the following imaginary experiment, an idealization of the experiment of electron diffraction by a crystal. Let us imagine a screen impermeable to electrons, in which two slits are cut. On observing the passage of a beam of electrons through one of the slits, the other being covered, we obtain, on a continuous screen placed behind the slit, some pat- tern of intensity distribution; in the same way, by uncovering the second slit and covering the first, we obtain another pattern. On observing the passage of the beam through both slits, we should expect, on the basis of ordinary classical ideas, a pattern which is a simple superposition of the other two: each electron, moving in its path, passes through one of the slits and has no effect on the electrons passing through the other slit. The phenomenon of electron diffraction shows, however, that in reality we obtain a diffraction pattern which, owing to interference, does not at all correspond to the sum of the patterns given by cach slit separately. It is clear that this result can in no way be reconciled with the idea that electrons move in paths. Thus the mechanics which govems atomic phenomena-quantum mechanics or wave mechanics-must be based on ideas of motion which are fundamentally different from those of classical mechanics. In quantum mechanics there is no such concept as the path of a particle. This forms the content of what is called the uncertainty principle, one of the fundamental principles of quantum mechanics, discovered by W. Heisenberg in 1927. In that it rejects the ordinary ideas of classical mechanics, the uncertainty principle might be said to be negative in content. Of course, this principlc in itself does not suffice as a basis on which to construct a new mechanics of particles. Such a theory must naturally be founded on some positive asser- tions, which we shall discuss below (?). However, in order to formulate these assertions, we must first ascertain the statement of thc problems which confront quantum mechanics. To do so, we first cxamine the special nature of the interrelation between quantum mechanics and dassical mechanics. A more general theory can usually be formulated in a logically complete manner, independently of a less general theory which forms a limiting case of it. Thus, relativistic mechanics can be constructed on the basis of its owr fundamental prindples, without any reference to Newtonian mechanics. It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics. The fact that an electron has no definite path means that it has also, in itself, no other dynamical characteristics. Hence it is clear that, for a system composed only of quantum objects, it would be entirely impossible to construct any logically independent mechanics. The possibility of a quantitative description of the motion of an electron requires the presence also of physical objects which obey classical mechanics to a sufficient degree of accuracy. If an electron interacts with such a "classical object", the state ofthe latter is, generally speaking, altered. The nature and magnitude of this change depend on the state of the electron, and therefore may serve to characterize it quantitatively. |
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