Topic 4 Flashcards
Describe the very basic diagram of the Helium atom.
Nucleus with 2+ protons. Extends r1 to the first electron. Then e1 connects to e2 by r12. e2 connects back to the nucleus through r2.
What does the Hamiltonian tell you about?
Energy (PE&KE)
What does kinetic energy tell us?
How quickly it is changing positions
What does the Kinetic energy of the Hamiltonian equation look like?
-h^2/2m
Why is the kinetic energy term negative in the helium and hydrogen model?
Because there is an attraction between the proton and electron which makes it overall negative
What does the 1/r term mean in the hamiltonian for hydrogen and helium?
The negative sign indicates that the potential energy decreases as the distance between the electron and the nucleus decreases, reflecting the attractive nature of the electrostatic interaction. The term (1/r) represents the inverse relationship between the potential energy and the distance r1 , indicating that the potential energy becomes stronger as the electron gets closer to the nucleus.
Why is the Schrodinger equation ‘unsolveable’ for Helium?
The columbic repulsion term makes it impossible because it cares about both electron distances at the same time which isnt possible.
What is the variational method?
Since we cant find the true Psi, we find the trial wave function Phi that is a close estimate of the true energy
What are the variational parameters in the trial function?
Phi(alpha, beta, gamma,…)
How do you optimize the trial function?
By varying the parameter to minimize energy
What is the repulsion term?
(e^2/4piepsilon)(1/r12)
