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Quantum Mechanics: Binding Energies of Small Atoms

Calculate ionization energies of first ten atoms using momentum space electrostatistics. Explore Feynman Theorem, Hydrogenic wavefunction, and hydrogen molecule polarizability. Understand Non-Relativistic Quantum Mechanics formalism.

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Quantum Mechanics: Binding Energies of Small Atoms

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  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

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