Write down the ground state eigenfunction (and spin) of Helium.

In summary, the conversation is about finding the ground state eigenfunction for a helium atom. The person has found some old books with solutions, but they are difficult to understand. They also have a proof of the formula for the expectation energy of helium, but they are unsure how it relates to the ground state eigenfunction. They mention a textbook by Chris Foot and provide a formula for the total ground state eigenfunction, which is the product of the spin part and the spatial part.
  • #1
helpcometk
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Homework Statement


Already it is on title !


Homework Equations


attachents provide the most relevant equations i could find.


The Attempt at a Solution


I have found some old books written in 1920 decade ,dealing with this subject,but the solution they provide seems very hard understand,although it might be correct.

http://books.google.co.uk/books?id=...e&q=helium ground state eigenfunction&f=false

i have in my possesion proof of the formula for the expectation energy of helium atom.
But i don't know if and how could this be related to the ground state eigenfunction.
i can't really provide more relevant formulas ,but it must be appreciated that this is not an easy problem.
 

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  • #2
In the meantime i have found very important additional information using the textbook of chris foot called atomic physics.
The total groundstate eigenfunction ψ of helium must be the product of spin part and spatial part i.e

ψ= ψspin ψspatial= (according to this textbook) =( ms) (u1sunl) = (according to tables provided in this book i.e table 2.2 )= {√1/4π}{(z/a)3/2 (2e-p)}
 

1. What is the ground state eigenfunction of Helium?

The ground state eigenfunction of Helium is given by the wave function Ψ = (1/√2)[ϕ1s(1)ϕ1s(2) + ϕ1s(2)ϕ1s(1)], where ϕ1s represents the 1s orbital of the two electrons.

2. What is the spin of Helium's ground state eigenfunction?

The ground state eigenfunction of Helium has a spin of 0, as it is a singlet state with two electrons having opposite spins.

3. How does the ground state eigenfunction of Helium differ from that of Hydrogen?

The ground state eigenfunction of Helium differs from Hydrogen in that it takes into account the interaction between the two electrons, resulting in a more complex wave function.

4. Can the ground state eigenfunction of Helium be solved analytically?

Yes, the ground state eigenfunction of Helium can be solved analytically using the Schrödinger equation and the variational method.

5. What information does the ground state eigenfunction of Helium provide?

The ground state eigenfunction of Helium provides information about the spatial distribution and energy of the two electrons in the atom.

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