# Caculating ground state energy using GTO

1. Oct 10, 2015

### 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?

2. Oct 10, 2015

### blue_leaf77

What do you know about "variational principle"?

3. Oct 10, 2015

### alaa74

Just beginning the subject

4. Oct 10, 2015

### 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 $H$.

5. Oct 10, 2015

### alaa74

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