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Hamiltonian in atomic units 
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#1
Feb1811, 01:03 AM

P: 43

1. The problem statement, all variables and given/known data
So the question is I have to use some trial function of the form [tex]\sum c_if_i[/tex] to approximate the energy of hydrogen atom where [tex]f_i=e^{ar}[/tex] for some number a (positive real number). Note that r is in atomic unit. 2. Relevant equations Because r is in atomic unit, I think I should use the Hamiltonian in atomic unit, that is [tex]H = \frac{1}{2}\nabla^2 + \frac{1}{r}[/tex] or should I use the spherical Hamiltonian? I try to compute [tex]H_{ij} = \int_0^\infty f_iHf_j[/tex] but there will be the term [tex]\int_0^\infty f_1\frac{1}{r}f_2dr[/tex] which cannot be integrated (not converged). So what's wrong with the way I approach the problem? Thank you, 


#2
Feb1811, 03:06 AM

P: 206

might your coefficients be r dependent since they are in the full solution of the hydrogen like atom



#3
Feb2311, 02:59 PM

P: 51

[tex]
\int_0^\infty f_1\frac{1}{r}f_2dr [/tex] will converge if you change 1/r to 1/(r+eps) 


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