L18.2 Ground State Energy of Helium: Hamiltonian minimization (Part 4/4)

#QuantumCalculations #ElectronRepulsion #VariationalMethod #PhysicsForBeginners

0:00 - Introduction to Electron-Electron Repulsion Term
0:11 - Solving Integrals for I2 and Finalizing Expression
1:10 - Converting R2 Integral into R1
2:00 - Electron Repulsion Term in Spherical Coordinates
3:00 - Angular and Radial Integration for Ve
5:00 - Simplifying Ve and Intermediate Results
6:30 - Connecting Results with Bohr Radius and Energy Calculations
8:00 - Approximating Total Energy: Comparing with Experiment
9:30 - Importance of Hamiltonian Corrections
10:30 - Introducing the Optimization of Z
11:30 - Next Steps: Achieving Closer Agreement with Experiment

Lecture Notes:
https://drive.google.com/file/d/1QWyAGbBGEe8xuu9aqVYeUjbOTWgn13Y2/view?usp=sharing

Board Image:
https://drive.google.com/file/d/1CLt7zBm1aycz-f9NkoTjALnptDrvMFab/view?usp=sharing

In this lecture on quantum mechanics, we dive into the calculation of electron-electron repulsion terms and their contribution to the total energy of a system. Using integrals and wave functions derived from hydrogen-like atoms, we explore the approximations and simplifications that bring our theoretical calculations closer to experimental values. Special attention is given to solving integrals for Ve, simplifying expressions, and understanding the role of the Bohr radius. The lecture concludes with a preview of optimizing Z to further refine our model and achieve even closer alignment with experimental results. This session provides a detailed walkthrough of advanced quantum mechanics concepts, making it essential for students and enthusiasts seeking a deeper understanding of atomic systems.

Quantum mechanics lecture
Electron-electron repulsion
Calculating Ve Hamiltonian corrections
Quantum wave function
Hydrogen atom energy calculation
Bohr radius derivation
Advanced quantum mechanics tutorial
Optimizing atomic Z
Experimental and theoretical energy comparison

Видео L18.2 Ground State Energy of Helium: Hamiltonian minimization (Part 4/4) канала SAYPhysics