Caculating ground state energy using GTO

[alaa74]

Using the single-electron wave function ψ(r) = N*exp( −ζr² ) with ζ a variational parameter, how can we calculate the best approximation for the ground state energy of the hydrogen atom?

 

[blue_leaf77]

What do you know about "variational principle"?

 

[alaa74]

Just beginning the subject

 

[blue_leaf77]

Variational principle can be used to calculate the upper bound of the ground state of a system. This is because
$$
\langle \psi | H | \psi \rangle \geq E_g
$$
where $\psi$ is an arbitrary normalized state and $E_g$ the system's ground state whose Hamiltonian is $H$.

 

[alaa74]

Thank you. I was really lost. now I will work on the variational method to solve the homework . Thanks :-)