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phys documents (dragged) 58 - 52 Physics Formulary by ir...

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52 Physics Formulary by ir. J.C.A. Wevers For N particles the symmetric spatial function is given by: ψ S (1 , ..., N ) = ψ ( all permutations of 1 ..N ) The antisymmetric wavefunction is given by the determinant ψ A (1 , ..., N ) = 1 N ! | u E i ( j ) | 10.15.2 Molecules The wavefunctions of atom a and b are φ a and φ b . If the 2 atoms approach each other there are two possibilities: the total wavefunction approaches the bonding function with lower total energy ψ B = 1 2 2( φ a + φ b ) or approaches the anti-bonding function with higher energy ψ AB = 1 2 2( φ a - φ b ) . If a molecular-orbital is symmetric w.r.t. the connecting axis, like a combination of two s-orbitals it is called a σ -orbital, otherwise a π -orbital, like the combination of two p-orbitals along two axes. The energy of a system is: E = ψ | H | ψ ψ | ψ . The energy calculated with this method is always higher than the real energy if ψ is only an approximation for the solutions of H ψ = E ψ . Also, if there are more functions to be chosen, the function which gives the lowest
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