Variational Method to determine the trial function for atoms

 The Variation Method

  - Variational treatment of the Hydrogen-like atom
  - Variational treatment of the Helium atom
  - The linear variation method : Example
  - The hydrogen atom in an external electric field

 http://research.chem.psu.edu/lxjgroup/download_files/chem565-c8.pdf

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Variational Method for ground and excied states og Hydrogen atom

- Introduction
- Ground state
- Excited state
- Why Not Full Variation?

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The Variational Method

* Degenerate perturbation theory
 The coupled quantum well
* The Variational method
 The triangular well

https://nanohub.org/resources/5007/download/degenerate_pt.pdf

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 The variational theory and the variational principle

Example I: The harmonic oscillator
Example II: The harmonic oscillator revisited

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Lecture I : The variational principle

I. THE APPROXIMATE WAVEFUNCTION
II. VARIATION WITH RESPECT TO COEFFICIENTS (LINEAR VARIATION) AND LAGRANGE MULTIPLIERS
III. AN EXAMPLE : DELTA-FUNCTION POTENTIAL

http://www.physics.metu.edu.tr/~hande/teaching/741-lectures/lecture-01.pdf

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1 Lecture 2: The helium atom

1.1 The hamiltonian
1.2 Solving H0
1.3 The variational method, take 1: no variation
1.4 The variational method, take 2: an improved trial wavefunction