This is based on the author'sfollowing two principles: (i) if a textbook were so perfectly arranged that leaves nothing to be desired, it would make the readers feel that the scientific discovery is so mystical that they lose passion of creativity; (ii) if a course were so purely presented that highes on a perfect axiomatics without mention of incomplete doctrine in history of science, it would lose the chance of training students' power of creativity. College students should cultivate their ability of capturing knowledge and attain the power of employing knowledge in addition to the simple task of absorbing knowl-edge. So the author tried to adopt second-person pronoun in presenting this course. According to the author's teaching experience, some mediate steps of mathematical formulation that beginners are not able to figure out frequently, are also given. In order to avoid too much content in class,some important examples are arranged as problems with solutions.

I Basic Concepts and Main Applications

1 The Discovery of Quantum Theory

 1.1 Blackbody Radiation and Planck's Hypothesis of Energy Quanta

 1.2 Photoelectric Effect and Einstein's Hypothesis of Light Quanta

 1.3 The Atomic Spectra and Bohr's Model of Atoms

2 Wavefunction and Schr6dinger Equation

 2.1 The de Broglie Hypothesis and Davisson-Germer Experiment

 2.2 Schrodinger Equation

 2.3 Stationary Solutions

 2.4 General Properties of Motion in One Dimension

 2.5 Bound States in Potential Well

2.5.1 Square Well of Infinite Depth

2.5.2 Square Well of Finite Depth

 2.6 The Harmonic Oscillator

 2.7 Tunnelling Effect

3 Operators and Heisenberg Uncertainty Relation

 3.1 Observables and Operators

 3.2 Hermitian Operators and Their Properties

 3.3 Some Example Operators

3.3.1 Momentum Operators and Their Eigenfunctions

3.3.2 Angular Momentum Operators and Their Eigenfunctions

3.3.3 Coordinate Representation and Momentum Representation

 3.4 Evaluation of the Expectation Values

 3.5 The Heisenberg Uncertainty Relation

3.5.1 Commutation Relations and Their Implications

3.5.2 Uncertainty Relation and the Minimum Uncertainty State

 3.6 The Time Evolution of Expectation Values

4 Motion in a Centrally Symmetric Field

 4.1 Three Dimensional Harmonic Oscillators

 4.2 The Feature of Motion in a Centrally Symmetric Field

 4.3 Spherical Waves and Plane Waves

 4.4 Motion in a Coulomb Field

 4.5 Hydrogen-like Energy Levels

 4.6 Hydrogen Atom and Hydrogen-like Ions

5 States and Heisenberg Equation

 5.1 Matrix Representation of Operators

 5.2 States and Their Representations

 5.3 The Heisenberg Equation

 5.4 Algebraic Approach for Harmonic Oscillator

 5.5 Algebraic Approach for Angular Momentum

II Developing Skills

6 Bound-State Perturbation and Corrections to Energy Levels

 6.1 Nondegenerate Perturbation TheOry

 6.2 Degenerate Perturbation Theory

 6.3 Stark Effect

7 Time-dependent Perturbation and Quantum Transitions

 7.1 Perturbation Depending on Time

 7.2 Transition Probability

7.2.1 Periodic Perturbation of Single Frequency

7.2.2 Transition to Continuous Spectrum

 7.3 Induced Absorption and Emission

 7.4 Einstein's Semi-phenomenological Theory for Spontaneous Emission

8 Scattering Theory for Elastic Collisions

 8.1 Scattering Amplitude and Cross Section

 8.2 Born Approximation

8.2.1 The Simplest Approach

8.2.2 Lippmann-Schwinger Equation

8.2.3 Scattering by Screened Coulomb Potential

 8.3 Partial-Wave Approach

8.3.1 Phase Shifts and Scattering Amplitudes for Centrally Symmetric Potentials

8.3.2 Neutron-Proton Scattering

8.3.3 The Center-of-Mass Frame and the Lab Frame

9 Motion in a Magnetic Field

 9.1 Schrodinger Equation for a Charged Particle in Electromagnetic Fields

 9.2 Electrons in a Uniform Magnetic Field

 9.3 Atoms in Magnetic Field and Zeeman Effect

 9.4 Electron Spin

 9.5 Spin-Orbit Coupling and the Fine Structure of Atomic Spectra

9.5.1 On Spin-Orbit Coupling

9.5.2 On the Fine Structure of Atomic Spectra

10 Identical Particles and Pauli Exclusive Principle

  10.1 Permutation Symmetry and the Indistinguishability of Identical Particles

  10.2 Noninteracting Systems, Pauli Exclusive Principle

  10.2.1 Two-particle Systems

  10.2.2 N-particle Systems

  10.3 Interacting Systems

  10.3.1 Helium Atom, Hund's Rule

A Matrix and Vector Space

B δ-function

C Confluent Hypergeometric Function

D Orbitals for d-Electrons

E Lab Frame and Center-of-mass Frame

F On an Integral

G Time Reversal and Kramers Degeneracy