1. Binding Energies of Small Atoms by Momentum Space Electrostatistics Soydaner Ülker 07 June 2010

2. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Synopsis SCOPE KEY CONCEPTS & NOTATION FORMALISM IMPLEMENTATION CONCLUSION QUESTIONS & ANSWERS Estimated duration 20 min.

3. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Problem: Scope Key Concepts & Notation Formalism ImplementationConclusion Subject Field: Calculate Ionization Energy Base: Non Relativistic Quantum Mechanics Assumptions: First Ten Atoms Technique: Momentum Space Calculations Feynman Theorem – Electrostatics Hydrogenic Wavefunction 55 ionization energies

4. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Scope Key Concepts & Notation Formalism ImplementationConclusion Non Relativistic Quantum Mechanics Time Independent Schrodinger Equation Physical System Quantum State Hydrogenic wavefunction Form Factor Energy Momentum Space Calculation Eigenvalues – eigenfunctions Probability Density

5. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Scope Key Concepts & Notation Formalism ImplementationConclusion Non Relativistic Quantum Mechanics Form Factor Energy Momentum Space Calculations Convolution Theorem The inverse Fourier transform of a product of two or more Fourier transforms is the convolution integral. Position to Momentum Fourier Transform Coulomb potential in momentum space is

6. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Scope Key Concepts & Notation Formalism ImplementationConclusion Form Factor Non Relativistic Quantum Mechanics Momentum Space Calculation Energy WHATofWHEREForm Factor chargeprotonpoint chargeelectron 1s Magnetic dipoleprotonpoint Magnetic dipoleelectron 1s

7. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Electrostatics, Coulomb Potential Scope Key Concepts & Notation Formalism ImplementationConclusion Non Relativistic Quantum Mechanics Momentum Space Calculation Form Factor Energy Hydrogen Energy Levels Bohr Radius Hydrogen Ground State Energy

8. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Scope Key Concepts & Notation Formalism ImplementationConclusion symmetric concentric symmetric concentric identical 6 fold integral ! Energy Minimization Virial Theorem Procedure 6 fold Double convolution 3 fold Concentric Symmetric Coulomb 1 fold

9. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Scope Key Concepts & Notation Formalism ImplementationConclusion Hydrogen Atom: Concentric, Spherically Symmetric, Coulomb Proton Size Magnetic Dipole Hydrogen Helium Other Contributions: Lithium Atom: 3 e in 1s stateTheory: 230.234 eV, Exp: 203.481 eV, err: - 13.15% Non Spherical Symmetry: x electron identical particle, fermion Pauli 2 e in 1s, 1e in 2s state err: + 3.27% Spherical Harmonics: Y 10, Y 00

10. Binding Energies of Small Atoms by Momentum Space Electrostatics 07 June 2010 Soydaner Ülker Scope Key Concepts & Notation Formalism ImplementationConclusion QUESTIONS & ANSWERS All Energies 55 Model deviates Hydrogenic wavefunction One independent variable, λ Other energy contributions Drawbacks Hydrogen Molecule: Polarizability