Quantum Physics Question - Second Year University level.

[coffeem]

Hi there,

I have some questions which I cannot solve from my Quantum book. I would appretiate some hints as to how they should be solved. Thanks.

Question

The antisymmetric eigenfunction of the helium atom can be written in the form UA - C(uab-uba), where uab and uba are orthonormal. Show that the normalisation constant C = 1/root(2).

 

[tiny-tim]

Hi coffeem!

The antisymmetric eigenfunction of the helium atom can be written in the form UA - C(uab-uba), where uab and uba are orthonormal. Show that the normalisation constant C = 1/root(2).

well, that means you have to prove that (uab-uba)(uab-uba)* = 2

 

[coffeem]

Hi coffeem!


well, that means you have to prove that (uab-uba)(uab-uba)* = 2

Thanks for your help, I really do appreciate it. I can expand the brackets and get:

UabUab + UbaUba = 2 (since UabUba = 0)

So would a reasonable answer be:

Since (Uab-Uba)^2 is 2, to normalise this to 1, we must divide the eigenfunction by the square root of this?

Thanks.

 

[tiny-tim]

Thanks for your help, I really do appreciate it. I can expand the brackets and get:

UabUab + UbaUba = 2 (since UabUba = 0)

So would a reasonable answer be:

Since (Uab-Uba)^2 is 2, to normalise this to 1, we must divide the eigenfunction by the square root of this?

Thanks.

Yes, except I'd say "we must divide it by the square root" …

any multiple of (Uab-Uba) is an eigenfunction.