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L_Variat_method - TWO INTERACTING ELECTRONS NO SEPARATION...

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No separation of variables—no exact solution
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Approximate Methods
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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).
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Variational Methods: example: Harmonic oscillator Variational Principle
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Variational Methods: example: Harmonic oscillator Variational Principle Insert value of γ obtained by minimization into expression of χ and find ground state wavefunction
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More general variational treatment For example….
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END Detour: BACK TO HELIUM ATOM
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Unformatted text preview: TWO INTERACTING ELECTRONS: NO SEPARATION OF VARIABLES χ 1 and χ 2 are written as products of known functions φ . Note that each φ depends only on r 1 OR r 2 , not on both r 1 AND r 2 χ 1 and χ 2 are basis functions; c 1 and c 2 are variational parameters to be determined χ 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:...
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