1 The Basics of ntum Mechanics for the Weakest Bound Electron(WBE)Theory 1.1 The Wave Particle Duality 1.2 The Uncertainty Principle 1.3 The Schrodinger Equation 1.4 Electron Spin and Spin Orbital(3,6-8) 1.5 The Indistinguishability of Micro Identical Particles 1.6 Pauli Exclusion Principle and Periodic Table 1.7 One of the Approximation Methods in ntum Mechanics-The Variation Method References 2 The Weakest Bound Electron Theory(1) 2.1 TheConceptoftheWeakestBoundElectron 2.2 Ionization Process and Aufbau-Like Process is Reversible . The One-Electron Hamiltonian for the Weakest BoundElectron ..1 The Non-Relativistic One-Electron Hamiltonianforthe Weakest Bound Electron ..2 The Treatment of Magnetic Interaction BetweenElectrons .. Relativistic Hamiltonian 2.4 The neElectron Schrodinger Equation of the Weakest Bound Electron 2.5 TheKeyPoints oftheWBETheory References 3 TheWeakestBoundElectronTheory(2) 3.1 Potential Function 3.2 The Solution ofthe Radial Equation 3.2.1 Spherical Harlnonic 3.2.2 Generalized Laguerre Functions 3.. Restore the Form of Hydrogen and Hydrogen Like Atoms 3.2.4 The Definition and Properties of Generalized Laguerre Functions 3.2.5 The Proof of the Satisfaction of Hellmann-Feynman Theorem 3.3 Matrix Element and Mean Value of Radial Operator rk 3.4 The Exact Solutions of Scattering States in WBEPM Theorv 3.5 The Formula for the Calculation of Fine Structure 3.6 Calculation of Spin-Orbit Coupling Coefficient 3.7 Relation Between the WBEPM Theory and Slater-TyDe Orbitals References 4 The Application ofthe WBE Theory 4.1 Ionization Energy(1-10) 4.1.1 Introduction 4.1.2 Iso-spectrum-level Series and the Differential Law of Ionization Energy in the Series 4.1.3 Calculation ofIonization Energy 4.1.4 The Successive Ionization Energies of the 4f Electrons for the Lanthanides(10) 4.2 Energy Level(39-50) 4.2.1 Introduction 4.2.2 FormulaeforCalculatingEnergyLevels 4.. Methods for Parameter Characterization 4.2.4 Examples 4.3 Calculation of Oscillator Strength,Transition Probability and Radiative Lifetime(88-104) 4.3.1 Introduction