量子力学

Preface

Ⅰ.Brief review of historical development

1.Black boay radfatlon

2.Photoelectric effect

3.Specific heat of solids

4.Compton effect

Problems

Ⅱ.Uncertainty and complementarily

1.Einstein relations and Bohr complimentarity principle

2.Wave-particle duality and quantum behavior

3.De Broglie relation and Heisenberg uncertainty relation

4.Further remarks on the uncertainty principle

Problems

Ⅲ.The Schr6dinger wave equation

1.Postulates of quantum mechanics

2.The SchrOdinger equation for free particles

3.Probability distributions

4.Operators and expectation values

5.Motion of a free wave packet

6.Schr6dinger equation for a particle in external fields

7 Schr6dinger equation for a system+of interacting particles

Problems

Ⅳ.Heisenberg equation of motion and commutators

1.Heisenberg equation of motion

2.Commutation relations

ProblerDs

Ⅴ.Symmetry properties and conservation laws

1.Uniformity of time

2.Uniformity of space

3.Isotropy of space

4.Discrete transformation

5.Reduction of the two-body problem

Problems

Ⅵ.Eigenfunctions and eigenvalues

1.Stationary states

2.Spectrum of the Hamiltonlan

3.Diracs &function

4.Orthonormality and completeness

5.Density of states

6.Linear vector space

7.Simultaneous eigenfunctions and compatible observables

8.Probability amplitudes

Problems

Ⅶ.The classical limit and WKB method

1.Ehrenfest theorem

2.Classical limit of Schr6dinger equation

3.The semi-classical approximation for stationary states

4.The quantization rule of Bohr and Sommerfield

Problems

Ⅶ.lllustrative examples in one dimension

1.Square well potential

2.Seatterirg from the square well-resonances and virtual states

3.Periodic potential-Kr0nig:Penne: model

4.The 3 functiofl potentidl

5.Linear harmonic oscillator

Problems

Ⅸ.Illustrativeexamples in three dimensional space

1.The wave equation in spherical coordinates

2.Symmetry properties of the central field problem

3.Angular momentum eigenstates

4.Free particle motion with a definite

5.Isotropic square well

6.Hydrogen atom ;

7.Degeneracy of hydrogen energy levels

8.Electron in magnetic fields--a cylitidfial field problem

9.Examples in the confined and low-dimensionM space

Problems

Ⅹ.Angular momentum

1.Matrix representation of angular momentum operators

2.Spin eigenvectors

* 3.Coupling of two angular momentum vectors

4; Rotation matrices

5.Arbitrary rotation of a rigid body

Problems

Ⅺ.Unitary transformation

1.States and operators

2.Unitary operators and unitary transformations

3.Observables in different representations

* 4.,Schr6dinger, Heisenberg and interaction pictures

* 5.The interaction picture

6.Pure and,mixed states

Problems

Ⅻ.Approximation methods

1Variation method

2.Pert urbationtheory for nonrdegenerate stationary states

3.Yalidity of the perturbation method

4.Perturbation theory for degenerate states

5.Eine structureof hydrogen atomic spectra

6.Atoms in external magnetic fields

Problem,s

ⅩⅢ.Many-electron systems

1.Indistinguishability and Pauli principle

2.Symmetrization and anti-symmetrization of wave functions

3.Ground state of helium atom

4.Excited states of helium atom

5.Slater determinant for many-electron atoms

6.Hartree-Fock method

7.Statistical model of Fermi-Thomas

Problems

ⅩⅣ.Theory of time-dependent perturbation

1.Time-dependent perturbation

2.Transition probabilit_y pet: unit time

3.Adiabatic and sudden approximation

4.Induced emission, absorption and spontaneous emission

5.Multipole radiation and selection rules

6.Lifetime and width of excited levels

7.Photoelectric effect

8.Magnetic resonance

9.Oscillating strength Problems

ⅩⅤ.Theory of scattering

1.General theory of elastic scattering

2.Green function for a free particle

3.The Born approximation

4.Validity criteria for the Born approxirnition

5.Method of partial waves

6.Eikonal approximation

7.Elastic scattering from the Coulomb potential

8.Generaltheory of inelastic gcattering--The Eipman-Schwingwer formulation

9.Scattering fromcomplex targefs

Problems

References

Index

《量子力学》是在作者长期的科学研究和多年执教中，吸取美国大学教学特点，结合中国高校教学改革的实际情况编著的。内容适合读者由浅入深的学习，对量子力学的抽象理论，通过理论阐述和具体事例对照，更易于理解和掌握。讲授基本知识的同时，本书也介绍了科学研究的前沿知识，使读者深入了解目前量子力学理论的发展状况。《量子力学》适合物理专业本科生及研究生学习使用，也可做为科研人员参考使用。

《量子力学》（Quantum Mechanics）是研究微观粒子的运动规律的物理学分支学科，它主要研究原子、分子、凝聚态物质，以及原子核和基本粒子的结构、性质的基础理论，它与相对论一起构成了现代物理学的理论基础。量子力学不仅是近代物理学的基础理论之一，而且在化学等有关学科和许多近代技术中也得到了广泛的应用。