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Trolle
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1. The problem statement, all variables, equations and given/known data
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Hi guys. I am working on solving the stationary Schrôdinger equation of the Helium atom by the variational method using a Slater determinant constructed from Slater type 1s orbitals, and in that respect i need to solve the Coulomb integral:
[tex] J = \int_ {R^3} \int_{R^3} \frac{e^{-\zeta r_1}e^{\zeta r_2}}{|\vec{r_1}-\vec{r_2}|}d^3r_1 d^3r_2[/tex]
where [tex] \vec{r}_n [/tex] denotes the position of the n'th electron with respect to the nucleus and [tex] R^3 [/tex] denotes that the integral is over all three dimensional space wheras [tex]d^3 r[/tex] symbolises an infinitesemal volume element. [tex] r_n[/tex] is the distance between the n'th electron and the nucleus whereas [tex] \zeta [/tex] is the variational parameter ( a constant with respect to the integral).
I know this might be a bit difficult to solve, but if any of you could give a hint or direct me to appropriate (preferably free) reading i would be very happy.
Thanks - Mads
Edit: I may have posted this in the wrong thread. Sorry if that is the case - just ignore.
¨
Hi guys. I am working on solving the stationary Schrôdinger equation of the Helium atom by the variational method using a Slater determinant constructed from Slater type 1s orbitals, and in that respect i need to solve the Coulomb integral:
[tex] J = \int_ {R^3} \int_{R^3} \frac{e^{-\zeta r_1}e^{\zeta r_2}}{|\vec{r_1}-\vec{r_2}|}d^3r_1 d^3r_2[/tex]
where [tex] \vec{r}_n [/tex] denotes the position of the n'th electron with respect to the nucleus and [tex] R^3 [/tex] denotes that the integral is over all three dimensional space wheras [tex]d^3 r[/tex] symbolises an infinitesemal volume element. [tex] r_n[/tex] is the distance between the n'th electron and the nucleus whereas [tex] \zeta [/tex] is the variational parameter ( a constant with respect to the integral).
I know this might be a bit difficult to solve, but if any of you could give a hint or direct me to appropriate (preferably free) reading i would be very happy.
Thanks - Mads
Edit: I may have posted this in the wrong thread. Sorry if that is the case - just ignore.
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