Wave function for the Helium molecule

[LCSphysicist]

Homework Statement

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Relevant Equations

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I am having a trouble to understand why the helium's wave function (in which we are ignoring the electric interaction between the electrons, as well the motion and problems that arise in considering the nucleus in the wave function) can be written as the product of the wave function of both electron.

I mean, being the electron fermion particles, shouldn't it be written as:

$$\psi = (\psi_{(nlm)'}(r1)\psi_{nlm}(r2) - \psi_{(nlm)'}(r2)\psi_{nlm}(r1))/{\sqrt(2)}$$

?

 

[PeroK]

What don't you understand?

 

[LCSphysicist]

What don't you understand?

Instead the equation i gave, the book claims that the wave function is:
$$\psi = \psi_{nlm} \psi_{(nlm)'}$$

 

[PeroK]

Instead the equation i gave, the book claims that the wave function is:
ψ=ψnlmψ(nlm)′

View attachment 276760

He says explicity that is a solution of the SDE. He hasn't yet considered the anti-symmetrization requirement - which, in any case, requires consideration of the spin state.

 

[LCSphysicist]

He says explicity that is a solution of the SDE. He hasn't yet considered the anti-symmetrization requirement - which, in any case, requires consideration of the spin state.

Good point. That's it