PS 8 hint

# PS 8 hint - Problem 1 Hints Units The units the problem is...

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Problem 1 Hints: Units The units the problem is given to you in (angstrom and eV) is a convenient unit for visualizing the results of the calculation, but remember when you add the nuclei-nuclei repulsion term to your energy you need to use a consistent unit for the charge of an electron and a proton. Alternatively, you can transform into atomic units which are related to the units of the problem as: Atomic Unit Units From Problem Length 1 bohr radius 0.53 Angstrom Energy 1 hartree 27.2 eV In atomic units the charge of an electron is -1 and the charge of a proton is +1. So in atomic units the nuclei-nuclei repulsion is given by 1/R. Method for Solving To solve this problem you need to minimize the energy of the wavefunction with respect to two coefFcients while maintaining an overall normalization. Ψ = c vb [ φ A ( r 1 ) B ( r 2 ) + B ( r 1 ) A ( r 2 )] + c ion [ A ( r 1 ) A ( r 2 ) + B ( r 1 ) B ( r 2 )] One can solve this by calculating the energy in terms of the coefFcients, setting c vb = 1 and then taking a derivative with respect to c ion . It is equivalent to write the hamiltonian
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