html5-img
1 / 10

Binding Energies of Small Atoms by Momentum Space Electrostatistics

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

aelliott
Download Presentation

Binding Energies of Small Atoms by Momentum Space Electrostatistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Synopsis • SCOPE • KEY CONCEPTS & NOTATION • FORMALISM • IMPLEMENTATION • CONCLUSION • QUESTIONS & ANSWERS Estimated duration 20 min.

  3. Formalism Scope Implementation Conclusion Key Concepts & Notation Calculate Ionization Energy Problem: 55 ionization energies First Ten Atoms Subject Field: Momentum Space Calculations Technique: Feynman Theorem – Electrostatics Hydrogenic Wavefunction Assumptions: Base: Non Relativistic Quantum Mechanics

  4. Formalism Scope Implementation Conclusion Key Concepts & Notation Non Relativistic Quantum Mechanics • Time Independent Schrodinger Equation • Eigenvalues – eigenfunctions • Physical System Quantum State • Hydrogenic wavefunction • Probability Density Momentum Space Calculation Form Factor Energy

  5. Formalism Scope Implementation Conclusion Key Concepts & Notation Momentum Space Calculations Non Relativistic Quantum Mechanics • Position to Momentum • Fourier Transform Coulomb potential in momentum space is • Convolution Theorem The inverse Fourier transform of a product of two or more Fourier transforms is the convolution integral. Form Factor Energy

  6. Formalism Scope Implementation Conclusion Key Concepts & Notation Form Factor Non Relativistic Quantum Mechanics Momentum Space Calculation Energy

  7. Electrostatics, Coulomb Potential Formalism Scope Implementation Conclusion Key Concepts & Notation Non Relativistic Quantum Mechanics Momentum Space Calculation Form Factor Energy Hydrogen Energy Levels Bohr Radius Hydrogen Ground State Energy

  8. Formalism Scope Implementation Conclusion Key Concepts & Notation 6 fold symmetric 6 fold concentric 6 fold symmetric concentric 6 fold identical 6 fold integral ! Double convolution 3 fold Concentric Symmetric Coulomb 1 fold Energy Minimization Virial Theorem Procedure

  9. Formalism Scope Implementation Conclusion Key Concepts & Notation Hydrogen Atom: Concentric, Spherically Symmetric, Coulomb Other Contributions: Proton Size Magnetic Dipole Hydrogen Helium Lithium Atom: x 3 e in 1s state Theory: 230.234 eV , err: - 13.15% Exp: 203.481 eV , Pauli err: + 3.27% electron 2 e in 1s, 1e in 2s state identical particle, fermion Non Spherical Symmetry: Spherical Harmonics: Y10 , Y00

  10. Formalism Scope Implementation Conclusion Key Concepts & Notation • All Energies 55 • Model deviates • Hydrogenic wavefunction • One independent variable, λ • Other energy contributions • Drawbacks • Hydrogen Molecule: • Polarizability QUESTIONS & ANSWERS

More Related