Reference no: EM132181525
Assignment - Ground State of Helium Atom by Variational Method
What you need to do:
Choose a trial wave function and calculate E[ψ] and minimise it with respect to [ψ]. You need to do some preliminaries.
Use Xp(r→) = e-α_pr^2 (Gaussian)
with
α1 = 0.297104
α2 = 1.236745
α3 = 5.749982
α4 = 38.216677
Don't worry about how these were obtained.
So now your job is the following:
Step 1: Obtain expressions for Tpq, hpq, Spq and Qpqrs.
Step 2: Choose initial values for Cp(p = 1, 2, 3, 4). You can choose any values. But not all of them should be zero.
Step 3: Normalise Cp, by using equation (10).
Step 4: Calculate all the elements (4x4) of the matrix H using equation (9).
Step 5: Solve the generalised eigenvalue problem: HC = E'SC
Choose the lower eigenvalue to be E' and find its corresponding eigenvector Cnew.
Step 6: Calculate the error:
![41_figure.png](https://secure.expertsmind.com/CMSImages/41_figure.png)
Step 7: Normalise Cp by using equation (10). Accept E' as correct value, and use equation (6) to calculate E, using E' and Cp.
Try to find an expression for E, using E' from equation (6).
Attachment:- Assignment File.rar