L_Variat_method

L_Variat_method - TWO INTERACTING ELECTRONS: NO SEPARATION...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
No separation of variables—no exact solution
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Approximate Methods
Background image of page 2
Small Detour : apply approximate methods to known problems (i.e. problems for which we already found an exact, analytical solution), e.g. Harmonic Oscillator (HA).
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Variational Methods: example: Harmonic oscillator Variational Principle
Background image of page 4
Variational Methods: example: Harmonic oscillator Variational Principle Insert value of γ obtained by minimization into expression of χ and find ground state wavefunction
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
More general variational treatment For example….
Background image of page 6
END Detour: BACK TO HELIUM ATOM
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TWO INTERACTING ELECTRONS: NO SEPARATION OF VARIABLES 1 and 2 are written as products of known functions . Note that each depends only on r 1 OR r 2 , not on both r 1 AND r 2 1 and 2 are basis functions; c 1 and c 2 are variational parameters to be determined is our trial wavefunction Overlap matrix elements Hamiltonian matrix elements Secular determinant energy c 1 , c 2 wavefunction Secular determinant energy c 1 , c 2 wavefunction Special cases: E = Natural units:...
View Full Document

This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.

Page1 / 15

L_Variat_method - TWO INTERACTING ELECTRONS: NO SEPARATION...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online