Download presentation
Presentation is loading. Please wait.
Published byPatrick Richards Modified over 9 years ago
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
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.